Triangles

Problem 701

ection 1 Question 14, 6.1.58 Part 1 of 3 HW Score: 92.86\%
Points: 0 of 1
The figure shows a cable car that carries passengers from A to C . Point A is 1.3 miles from the base of the mountain. The angles of elevation from A and B to the mountain's peak are $21^{\circ}$ and $64^{\circ}$ , respectively. a. Determine, to the nearest tenth of a foot, the distance covered by the cable car. b. Find $a$ , to the nearest tenth of a foot, in oblique triangle $A B C$ . c. Use the right triangle to find the height of the mountain to the nearest tenth of a foot.

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Problem 702

$17 A B C$ is an isosceles right-angled triangle.
The area of the triangle is $162 \mathrm{~cm}^{2}$ Work out the value of $x$ .

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Problem 703

Triangles $A B C$ and $D E F$ are similar.
Find the indicated distance. Round to the nearest tenth. (Assume $a=11 \mathrm{in}, \mathrm{c}=10 \mathrm{in}$ , and $d=16 \mathrm{in}$ .) Find side $D E$ . $\square$ in.

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Problem 704

The sun is $25^{\circ}$ above the horizon. Find the length of a shadow cast by a building that is 100 feet tall (see figure). (Round your answer to two decimal places.) $\square$ ft

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Problem 705

Using a ruler and a pair of compabses, construct a right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm . You must show all of your construction lines.
Measure the angle opposite the base to the nearest degree.

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Problem 706

42 10) 45 2 54 5.4 20

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Problem 707

4. In the following triangle, what is NOT a possible value of $x$ ? A) 1 B) 3 C) 4 D) 6

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Problem 708

-3 Quiz The ratio of the measures of the sides of a triangle is $9: 7: 3$ . If the perimeter of the triangle is 266 inches, find the length of the shortest side.

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Problem 709

Solve the right triangle for the unknown sides and angles. Round $A=46.2^{\circ}, a=30$ $B=\square{ }^{\circ}$ $b \approx$ $\square$ $c \approx \square$ $\square$ Start over Check

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Problem 710

5.2 112 < Question 26, 5.2.53 > Find the measure of the side of the right triangle whose length is designated by the lower case letter c. HW Score: 67.65%, 23 of 34 points O Points: 0 of 1 B T 向 Save C 23 m C ப 33° A

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Problem 711

Part 1 of 3 (a) Find the run, rise, and slope given by triangle $A B C$ . run: $\square$ rise: $\square$ slope: $\square$

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Problem 712

16. Solve for $x$ and $y$ . Round to the tenths place if necessary.

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Problem 713

Solve the triangle. $\begin{array}{l} a=8, c=2, B=90^{\circ} \\ b=\square \end{array}$ $\square$ (Do not round until the final answer. Then round to the nearest tenth as needed.) $\mathrm{C}=$ $\square$ ${ }^{\circ}$ (Do not round until the final answer. Then round to the nearest degree as needed.) A = $\square$ $\square^{\circ}$ (Do not round until the final answer. Then round to the nearest degree as needed.)

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Problem 714

$23 < 2y - 9 < 26$

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Problem 715

Find the range of possible values for $x$ . $\qquad$
The range is $\square$ $<x<$ $\square$ (Simplify your answers.)

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Problem 716

Find the area and perimeter of $\triangle D E F$ .

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Problem 717

Enercice $A B C$ est un triangle $M$ et $N$ . decux points telo que $\overrightarrow{A M}=\frac{3}{4} \overrightarrow{A B C t} \quad A \vec{N}=\frac{4}{3} \overrightarrow{A C}$ 1) faire la figure 2) on pose $\overrightarrow{B K}=x \overrightarrow{B C}, \overrightarrow{M K}=y \overrightarrow{M N}$ $(x, y) \in \mathbb{R}^{2}$ a-Montrer que $\overrightarrow{M K}=-\frac{3}{4} y \overrightarrow{A B}+\frac{4}{3}$ y $\overrightarrow{A C}$ B- Montrer que $\vec{B} \vec{M}^{2}=\left(\frac{3}{4} y-x\right) \overrightarrow{A B}+\left(x=\frac{4}{3} y\right) A C$ c. Montrer que $\overrightarrow{B M}=-\frac{1}{4} \overrightarrow{A B}$ 3) En considerant, les blifférentes exprescions de Br̈, determiner les valcurs de $x$ et $y$ .

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Problem 718

Activity 14.2: Bases and Heights of Triangles
1. The area of Triangle $B$ is 8 square units. Find the length of $b$ . Show your reasoning. $A=\frac{1}{2} \cdot b \cdot h$

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Problem 719

In a triangle, explain why angle trisectors can't trisect the opposite side.

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Problem 720

What happens when we bisect any triangle's angle? How does the angle bisector divide the opposite side? Prove it.

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Problem 721

Find the length $M P$ , where $M$ is the midpoint of $CA$ and $P$ is where the angle bisector of $\angle B$ intersects $CA$ .

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Problem 722

In $\triangle R S T$ , U divides $\overline{T S}$ in a $2:3$ ratio. M is the midpoint of $\overline{R U}$ . Find RV:RS.

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Problem 723

Find the height of a triangle with area 10.5 sq ft and base 6 ft. Options: 1.14 ft, 3.5 ft, 4.5 ft, 63 ft.

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Problem 724

Calculate the area of a right triangle with base 6 inches and height 6 inches using the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .

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Problem 725

Find $x$ and $y$ if the triangle angles are $(2y+6)°$ , $(3x)°$ , and $(8y-102)°$ with a total of $180°$ .

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Problem 726

Given $a=8$ , $b=2$ , and $A=10^{\circ}$ , find if this forms 1, 2, or no triangles. Solve any triangles formed.

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Problem 727

Find the perimeter and area of a triangle with height 11.2, sides 14.7, 13.4, and base 13.4. Round area to nearest tenth.

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Problem 728

One angle is $66^{\circ}$ , and the third angle is $57^{\circ}$ more than half the second angle. Find the second and third angles.

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Problem 729

Two similar triangles have sides $7x$ and $70$ for the first, and $120$ and $60$ for the second. Find $x$ .

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Problem 730

Calculate the area of a triangle with base 10m and height 8m using $Area = \frac{1}{2} \cdot base \cdot height$ .

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Problem 731

Consult the figure. To find the length of the span of a oroposed ski lift from $A$ to $B$ , a surveyor measures the angle DAB to be $25^{\circ}$ and then walks off a distance of $L=1000$ feet to $C$ and measures the angle $A C B$ to be $15^{\circ}$ . What is the distance from $A$ to $B$ ?
The distance from $A$ to $B$ is approtmately $\square$ feet. (Do not round until the final answer. Then round to two decimal places as needed.)

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Problem 732

Points $A$ and $B$ are separated by a lake. To find the distance between them, a surveyor locates a point $C$ on land such than $\angle C A B=52.1^{\circ}$ . Find the distance across the lake from $A$ to $B$ .
NOTE: The triangle is NOT drawn to scale. distance $\approx$ $\square$ ft
Enter your answer as a number; your answer should be accurate to 2 decimal places.

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Problem 733

The diagram shows a triangle.
What is the value of $s$ ? $s=\square^{\circ}$

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Problem 734

The diagram shows a triangle.
What is the value of $u$ ? $u=$

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Problem 735

Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. $a=6, b=4, A=70^{\circ}$
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.)

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Problem 736

The right triangle below has legs of length $a=10$ and $b=7$ . The hypotenuse has length $c$ .
Answer the questions below to find how $a, b$ , and $c$ are related.
Part 1: Compute the total combined area of the four triangles: Part 2: Compute the area of the large (outer) square: $\square$
Part 3: Using your answers in Parts 1 and 2, find the area of the small (inner) square. $c^{2}=$ $\square$ Part 4: We are given the side lengths $a=10$ and $b=7$ . Compute $a^{2}+b^{2}$ . $a^{2}+b^{2}=$ $\square$

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Problem 737

3. (15 pts) Given is that $A=38^{\circ}$ and $b=19 \mathrm{~cm}$ and $c=22 \mathrm{~cm}$ . Solve the triangle $A B C$ . Round measures to 1 decimal place if necessary.

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Problem 738

Triangle $D E F$ is formed by connecting the midpoints of the side of triangle $A B C$ . The lengths of the sides of triangle $A B C$ are shown. Find the perimeter of triangle $D E F$ . Figures not necessarily drawn to scale.

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Problem 739

Triangle $U V W$ is formed by connecting the midpoints of the side of triangle RST. The lengths of the sides of triangle $R S T$ are shown. What is the length of $\overline{W V}$ ? Figures not necessarily drawn to scale.

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Problem 740

Which of the following sets of numbers could represent the three sides of a triangle?
Answer $\{13,25,40\}$ $\{10,16,25\}$ Submit Answer $\{6,18,25\}$ $\{13,22,35\}$

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Problem 741

2. Дан треугольник $A B C: A(2 ; 3), B(6 ;-5), C(0 ; 0)$ . Составьте уравнение средней линии $M N$ , где $M$ и $N$ - середины сторон $A B$ и $B C$ соответственно.
3. Для данной системы векторов

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Problem 742

For the right triangles below, find the exact values of the side lengths $a$ and $d$ . If necessary, write your responses in simplified radical form. $a=$ $\square$ $d=$ $\square$

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Problem 743

rieți rezolvările complete.
1. In triunghiul $A B C, A D \perp B C, D \in B C$ , iar punctele $M, N$ și $P$ sunt mijloacele laturilor $A B, A C$ , respectiv $B C$ . Demonstrați că $M N P D$ este trapez isoscel.

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Problem 744

Which best describes the triangle? obtuse and isosceles acute and scalene right and isosceles acute and isosceles

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Problem 745

Triangle - Interior Angles Find the measure of the indicated angle in each triangle. 1)
21 3) $m \angle U=$ $\qquad$ $m \angle B=$ $\qquad$

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Problem 746

Consider a triangle $A B C$ like the one below. Suppose that $A=84^{\circ}, B=36^{\circ}$ , and $c=44$ . (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth. If there is more than one solution, use the bution labeled "or". $c=$ $\square$ , $a=$ $\square$ $\square$

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Problem 747

16) Solve for the value of $x$ . $x=1 \frac{2}{5}$ or 1.4 $x=5 \frac{3}{5}$ or 5.6 $x=2 \frac{4}{5}$ or 2.8 $x=1$ $x=4 \frac{4}{5}$ or 4.8
17) Using the value of $x$ from question 16 , find the measure of $\angle A$ . $m \angle A=130^{d} e g$ $m \angle A=75^{d} \mathrm{eg}$ $m \angle A=65^{d} \mathrm{eg}$ $m \angle A=110^{\prime} \mathrm{eg}$ $\mathrm{m} \angle A=150^{\mathrm{d}} \mathrm{eg}$

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Problem 748

20) Classify the triangle by congruence. isosceles scalene adjacent equilateral vertical 21) Classify the triangle by angle measure. complementary right acute supplementary

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Problem 749

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg: WI cm Length of the longer leg: $\square$ cm
Length of the hypotenuse: $\square$ cm

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Problem 750

7. The hypotenuse of a right triangle is 15 cm . If the 2 other sides differ by 3 cm , what are their lengths?

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Problem 751

For the right triangles below, find the exact values of the side lengths $d$ and $c$ . If necessary, wite your responses in simplified radical form.

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Problem 752

Find the length of side $a$ to the nearest tenth of a meter:
Law of Cosines: $a^{2}=b^{2}+c^{2}-2 b c \cdot \cos A$

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Problem 753

5377cd673btesfib5tda18248e
Desmos | Beautition. The National Archive. Answer Attempt 1 out of 6

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Problem 754

6. Classify the triangle with the following side lengths: $20,21,29$

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Problem 755

Deux repères $A$ et $B$ sont inaccessibles. Calculer la distance $A$ et $B$ entre ces deux points à partir des relevés suivants. Vos calculs doivent être faits au mètre près. $\begin{aligned} \mathrm{m} \overline{P P}^{\prime} & =450 \mathrm{~m} \\ \mathrm{~m} \angle A P^{\prime} P & =69^{\circ} \\ \mathrm{m} \angle A P P^{\prime} & =96^{\circ} \\ \mathrm{m} \angle B P P^{\prime} & =66^{\circ} \\ \mathrm{m} \angle B P^{\prime} P^{\prime} & =103^{\circ} \end{aligned}$

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Problem 756

Use the Law of Sines to find the length of each side of the parallelogram. Round to the nearest tenth. a. $A B \approx$ $\qquad$ cm b. $A D \approx$ $\qquad$ cm c. $D C \approx$ $\qquad$ cm d. $B C \approx$ $\square$ type your answercm olu

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Problem 757

1. If $J$ is the centroid of $\triangle C D E, D E=52, F C=15$ , and $H E=14$ , find each measure. $\begin{aligned} D G & =26 \\ G E & =26 \\ D F & =17.33 \\ C H & =5 \\ C E & =4.67 \end{aligned}$ Show Your Work

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Problem 758

Find the area of the triangle formed by the lines: $y=-2x+15$ , $y=-\frac{1}{2}x+3$ , and $y=x+3$ .

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Problem 759

Find the length of one leg of a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle with hypotenuse $22 \sqrt{2}$ units.

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Problem 760

Triangles $ABC$ and $DEF$ are similar. If $DEF$ has an area of 6 sq ft, find the area of $ABC$ with sides 12 ft and 4 ft.

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Problem 761

A painter is painting a right triangle gable with sides $8' - 4"$ and $8' - 4"$ . What is the area to paint, rounded to the nearest hundredth?

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Problem 762

Find the perimeter of a right triangle with sides 24 and 32. Round your answer to the nearest hundredth.

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Problem 763

A ladder leans against a wall at $60^{\circ}$ . The base is $2 \mathrm{~m}$ from the wall. Find the wall height and ladder length. $[\sin 60=0.866, \cos 60=0.5, \tan 60=1.732]$

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Problem 764

Find $A C$ in a triangular prism where angle $B P C=90^{\circ}$ . Also, find angle $x$ if $24 \tan x=\sqrt{3}$ .

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Problem 765

A baseball player in center field is approximately 350 feet from a television camera that is behind home plate. A batter hits a fly ball that goes to the wall 420 feet from the camera (see figure). The camera turns $8^{\circ}$ to follow ti How far (in ft ) does the center fielder have to run to make the catch? (Round your answer to one decimal place.) (i) $\square$ ft

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Problem 766

State if each triangle is acute, obtuse, or right. 3) $\begin{array}{c} 12^{2}+2^{2}=12 \mathrm{~cm} \\ 13^{2}=169 \end{array}$ 4)
Find the missing side. Round to the nearest tenth. 5) 6)

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Problem 767

(2) Part A:
Calculate the height of the triangle to the neares! tenth of a meter. A. 10.9 m B. 12.9 m C. 15.3 m D. 16.7 m

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Problem 768

Solve for $x$ in the triangle. Round your answer to the nearest tenth. $x=$

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Problem 769

Question 5 of 10 Is $\triangle A B C \sim \triangle D E F$ ? If so, identify the similarity postulate or theorem that applies. A. Similar - AA B. Similar-SSS C. Similar-SAS D. Cannot be determined

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Problem 770

Find the area of $\triangle U V W$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth. $\square$ $\mathrm{km}^{2}$

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Problem 771

One leg of a right triangle is 3 feet longer than the other leg. The hypotenuse is 15 feet. Find the dimensions of the triangle.

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Problem 772

The line segment shown in the xy-plane represents one of the legs of a right triangle. The area of this triangle is $48\sqrt{13}$ square units. What is the length, in units, of the other leg of this triangle?
A 16 B 32 C $3\sqrt{13}$

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Problem 773

Solve for x and find angle D. $x^{\circ}$ x = Angle D =

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Problem 774

$9a-4$ A P $5a+5$ Y $6a-1$ T Find $AY$ .

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Problem 775

What is the value of z? $27z-25^\circ$ $38^\circ$ $23z+33^\circ$ $z=$

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Problem 776

10. A beam is to be kept horizontal by a cord. In which of the four situations shown below will the tension in the cord be least? A. B. C. D.

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Problem 777

$\angle W X Z \cong \angle Y X Z .$
Which term describes $\overline{X Z}$ ? median angle bisector altitude none of these

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Problem 778

A 25-foot footbridge has diagonal supports at a $65^{\circ}$ angle. Find the length $x$ of a diagonal support. $x \approx$ feet

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Problem 779

Find the height of a triangle with area $A = 35$ in² and base $b = 7$ in using $A = \frac{1}{2} b h$ .

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Problem 780

Create a net for a triangle and a pyramid shape.

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Problem 781

A bucket has 9 shapes: triangle, square, rectangle, rhombus, parallelogram, trapezoid, pentagon, hexagon, octagon. Find the probability of selecting each shape.

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Problem 782

Find the perimeter of an equilateral triangle with sides measuring $1 \frac{3}{4}$ inches each.

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Problem 783

In isosceles triangle $ABC$ with $\overline{AB} \cong \overline{AC}$ , find $\angle CAB$ . Options: $50^{\circ}$ , $89^{\circ}$ , $115^{\circ}$ , $43^{\circ}$ .

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Problem 784

In isosceles triangle $ABC$ , if $\angle CAB = 25^{\circ}$ , find $\angle ABC$ . Options: $25^{\circ}$ , $77.5^{\circ}$ , $155^{\circ}$ , $65^{\circ}$ .

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Problem 785

Two right triangles, $ABC$ and $ABD$ , share side $AB$ . Given $\angle C = 63^{\circ}$ , $BC = 24$ , and $\angle ABD = 60^{\circ}$ , find $x$ (length of $AD$ ) and $h$ (height from $A$ to $BC$ ). Round to the nearest tenth.

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Problem 786

Given triangles ABC and DBC, where DBC is a right triangle with height 8. Find the area ratio of triangles AEB and DEC.

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Problem 787

Calculate the area of a triangle with base 6 units and height 5 units using the formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$ .

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Problem 788

2. Find the perimeter of a square if the length of its diagonal is 16 cm. Round to the nearest tenth.
A. 512.0 cm B. 45.3 cm C. 128.0 cm D. 90.5 cm
3. Three checkpoints X, Y, and Z are placed in the ocean to mark a sailboat race. Contestants start at X, sail to checkpoint Y and Z, and then return to checkpoint X. The location of the checkpoints and the racecourse are shown below.
$2.8$ miles $40^\circ$ $56^\circ$
What is the distance between checkpoint X and checkpoint Z to the nearest tenth of a mile?

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Problem 789

A triangular traffic island has sides $24.5,14.2$ , and 11.6 . What are the angles at the corners?
The angle across from the side 24.5 is $\square$ ${ }^{\circ}$ . (Round to the nearest tenth as needed.)

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Problem 790

Two sides of a sloped ceiling meet at an angle of $115.6^{\circ}$ . If the distances along the sides to the opposite walls are 11.5 ft and 14.7 ft , what length of bearn is needed to join the walls?
A $\square$ ft beam is needed to join the walls. (Round to the nearest tenth as needed.)

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Problem 791

If $m\angle DEG = m\angle D + m\angle G + 41^{\circ}$ , what is $m\angle EFG$ ?

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Problem 792

2. $30$ $45^\circ$ $\frac{30}{\sqrt{2}} = \frac{\sqrt{2}}{\sqrt{2}}$ x = \text{} y = \text{}

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Problem 793

The triangle $PQR$ , the measure of angle $P$ is $(3x + 5)^{\circ}$ , the measure of angle $Q$ is $(2x + 9)^{\circ}$ . If side $QR$ is extended through point $R$ to point $S$ , and the measure of angle $PRS$ is $(x + y)^{\circ}$ , What is the value of $x + y$ ?

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Problem 794

Find the value of $x$ $x=32^{\circ}$ $x=212^{\circ}$ $x=90^{\circ}$ Type here to search

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Problem 795

Find the equation of a line through point $A(3,8)$ that is perpendicular to line segment $\overline{BC}$ . $y=\square x+$

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Problem 796

1 The triangle whose side lengths are $5 \mathrm{~cm} ., 5 \mathrm{~cm}$ ., - cm. is an isosceles triang (a) 12 (b) 11 (c) 10 (d) 9

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Problem 797

DUE Dec 6-11:59 pm i
In the diagram, which is not drawn to scale, $G$ is the incenter of $\triangle D E F$ and $m \angle E D F=42^{\circ}$ . Find $m \angle G D F$ . $\mathrm{m} \angle \mathrm{GDF}=$ $0^{\circ}$

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Problem 798

$A(8, 5, -6)$ , $B(4, 7, 9)$ , $C(2, 1, 6)$ ج) إذا كانت : فبرهن باستخدام المتجهات أن النقط $A$ , $B$ , $C$ تمثل رؤوس مثلث الزاوية

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Problem 799

$x^{\circ}$ $124^{\circ}$ Side of the triangle below has been extended to form an exterior angle of $124^{\circ}$ . Find the value of $x$ .

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Problem 800

Find the value of $x$ . $45^\circ$ $83^\circ$ $x^\circ$

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1 ...5 6 7 8 9 10

Triangles

Problem 701

Problem 702

17ABC17 A B C17ABC is an isosceles right-angled triangle.The area of the triangle is 162 cm2162 \mathrm{~cm}^{2}162 cm2 Work out the value of xxx.

Problem 703

Triangles ABCA B CABC and DEFD E FDEF are similar.Find the indicated distance. Round to the nearest tenth. (Assume a=11in,c=10ina=11 \mathrm{in}, \mathrm{c}=10 \mathrm{in}a=11in,c=10in, and d=16ind=16 \mathrm{in}d=16in.) Find side DED EDE. □\square□ in.

Problem 704

The sun is 25∘25^{\circ}25∘ above the horizon. Find the length of a shadow cast by a building that is 100 feet tall (see figure). (Round your answer to two decimal places.) □\square□ ft

Problem 705

Using a ruler and a pair of compabses, construct a right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm . You must show all of your construction lines.Measure the angle opposite the base to the nearest degree.

Problem 706

42 10) 45 2 54 5.4 20

Problem 707

4. In the following triangle, what is NOT a possible value of xxx ? A) 1 B) 3 C) 4 D) 6

Problem 708

-3 Quiz The ratio of the measures of the sides of a triangle is 9:7:39: 7: 39:7:3. If the perimeter of the triangle is 266 inches, find the length of the shortest side.

Problem 709

Solve the right triangle for the unknown sides and angles. Round A=46.2∘,a=30A=46.2^{\circ}, a=30A=46.2∘,a=30 B=□∘B=\square{ }^{\circ}B=□∘ b≈b \approxb≈ □\square□ c≈□c \approx \squarec≈□ □\square□ Start over Check

Problem 710

5.2 112 < Question 26, 5.2.53 > Find the measure of the side of the right triangle whose length is designated by the lower case letter c. HW Score: 67.65%, 23 of 34 points O Points: 0 of 1 B T 向 Save C 23 m C ப 33° A

Problem 711

Part 1 of 3 (a) Find the run, rise, and slope given by triangle ABCA B CABC. run: □\square□ rise: □\square□ slope: □\square□

Problem 712

16. Solve for xxx and yyy. Round to the tenths place if necessary.

Problem 713

Problem 714

23<2y−9<2623 < 2y - 9 < 2623<2y−9<26

Problem 715

Find the range of possible values for xxx. \qquadThe range is □\square□ <x<<x<<x< □\square□ (Simplify your answers.)

Problem 716

Find the area and perimeter of △DEF\triangle D E F△DEF.

Problem 717

Problem 718

Activity 14.2: Bases and Heights of Triangles1. The area of Triangle BBB is 8 square units. Find the length of bbb. Show your reasoning. A=12⋅b⋅hA=\frac{1}{2} \cdot b \cdot hA=21​⋅b⋅h

Problem 719

In a triangle, explain why angle trisectors can't trisect the opposite side.

Problem 720

What happens when we bisect any triangle's angle? How does the angle bisector divide the opposite side? Prove it.

Problem 721

Find the length MPM PMP, where MMM is the midpoint of CACACA and PPP is where the angle bisector of ∠B\angle B∠B intersects CACACA.

Problem 722

In △RST\triangle R S T△RST, U divides TS‾\overline{T S}TS in a 2:32:32:3 ratio. M is the midpoint of RU‾\overline{R U}RU. Find RV:RS.

Problem 723

Find the height of a triangle with area 10.5 sq ft and base 6 ft. Options: 1.14 ft, 3.5 ft, 4.5 ft, 63 ft.

Problem 724

Calculate the area of a right triangle with base 6 inches and height 6 inches using the formula: Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21​×base×height.

Problem 725

Find xxx and yyy if the triangle angles are (2y+6)°(2y+6)°(2y+6)°, (3x)°(3x)°(3x)°, and (8y−102)°(8y-102)°(8y−102)° with a total of 180°180°180°.

Problem 726

Given a=8a=8a=8, b=2b=2b=2, and A=10∘A=10^{\circ}A=10∘, find if this forms 1, 2, or no triangles. Solve any triangles formed.

Problem 727

Find the perimeter and area of a triangle with height 11.2, sides 14.7, 13.4, and base 13.4. Round area to nearest tenth.

Problem 728

One angle is 66∘66^{\circ}66∘, and the third angle is 57∘57^{\circ}57∘ more than half the second angle. Find the second and third angles.

Problem 729

Two similar triangles have sides 7x7x7x and 707070 for the first, and 120120120 and 606060 for the second. Find xxx.

Problem 730

Calculate the area of a triangle with base 10m and height 8m using Area=12⋅base⋅heightArea = \frac{1}{2} \cdot base \cdot heightArea=21​⋅base⋅height.

Problem 731

Problem 732

Problem 733

The diagram shows a triangle.What is the value of sss ? s=□∘s=\square^{\circ}s=□∘

Problem 734

The diagram shows a triangle.What is the value of uuu ? u=u=u=

Problem 735

Problem 736

Problem 737

3. (15 pts) Given is that A=38∘A=38^{\circ}A=38∘ and b=19 cmb=19 \mathrm{~cm}b=19 cm and c=22 cmc=22 \mathrm{~cm}c=22 cm. Solve the triangle ABCA B CABC. Round measures to 1 decimal place if necessary.

Problem 738

Triangle DEFD E FDEF is formed by connecting the midpoints of the side of triangle ABCA B CABC. The lengths of the sides of triangle ABCA B CABC are shown. Find the perimeter of triangle DEFD E FDEF. Figures not necessarily drawn to scale.

Problem 739

Triangle UVWU V WUVW is formed by connecting the midpoints of the side of triangle RST. The lengths of the sides of triangle RSTR S TRST are shown. What is the length of WV‾\overline{W V}WV ? Figures not necessarily drawn to scale.

Problem 740

Which of the following sets of numbers could represent the three sides of a triangle?Answer {13,25,40}\{13,25,40\}{13,25,40} {10,16,25}\{10,16,25\}{10,16,25} Submit Answer {6,18,25}\{6,18,25\}{6,18,25} {13,22,35}\{13,22,35\}{13,22,35}

Problem 741

Problem 742

For the right triangles below, find the exact values of the side lengths aaa and ddd. If necessary, write your responses in simplified radical form. a=a=a= □\square□ d=d=d= □\square□

Problem 743

rieți rezolvările complete.1. In triunghiul ABC,AD⊥BC,D∈BCA B C, A D \perp B C, D \in B CABC,AD⊥BC,D∈BC, iar punctele M,NM, NM,N și PPP sunt mijloacele laturilor AB,ACA B, A CAB,AC, respectiv BCB CBC. Demonstrați că MNPDM N P DMNPD este trapez isoscel.

Problem 744

$17 A B C$ is an isosceles right-angled triangle.
The area of the triangle is $162 \mathrm{~cm}^{2}$ Work out the value of $x$ .

Triangles $A B C$ and $D E F$ are similar.
Find the indicated distance. Round to the nearest tenth. (Assume $a=11 \mathrm{in}, \mathrm{c}=10 \mathrm{in}$ , and $d=16 \mathrm{in}$ .) Find side $D E$ . $\square$ in.

The sun is $25^{\circ}$ above the horizon. Find the length of a shadow cast by a building that is 100 feet tall (see figure). (Round your answer to two decimal places.) $\square$ ft

Using a ruler and a pair of compabses, construct a right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm . You must show all of your construction lines.
Measure the angle opposite the base to the nearest degree.

4. In the following triangle, what is NOT a possible value of $x$ ? A) 1 B) 3 C) 4 D) 6

-3 Quiz The ratio of the measures of the sides of a triangle is $9: 7: 3$ . If the perimeter of the triangle is 266 inches, find the length of the shortest side.

Solve the right triangle for the unknown sides and angles. Round $A=46.2^{\circ}, a=30$ $B=\square{ }^{\circ}$ $b \approx$ $\square$ $c \approx \square$ $\square$ Start over Check

Part 1 of 3 (a) Find the run, rise, and slope given by triangle $A B C$ . run: $\square$ rise: $\square$ slope: $\square$

16. Solve for $x$ and $y$ . Round to the tenths place if necessary.

$23 < 2y - 9 < 26$

Find the range of possible values for $x$ . $\qquad$
The range is $\square$ $<x<$ $\square$ (Simplify your answers.)

Find the area and perimeter of $\triangle D E F$ .

Activity 14.2: Bases and Heights of Triangles
1. The area of Triangle $B$ is 8 square units. Find the length of $b$ . Show your reasoning. $A=\frac{1}{2} \cdot b \cdot h$

Find the length $M P$ , where $M$ is the midpoint of $CA$ and $P$ is where the angle bisector of $\angle B$ intersects $CA$ .

In $\triangle R S T$ , U divides $\overline{T S}$ in a $2:3$ ratio. M is the midpoint of $\overline{R U}$ . Find RV:RS.

Calculate the area of a right triangle with base 6 inches and height 6 inches using the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .

Find $x$ and $y$ if the triangle angles are $(2y+6)°$ , $(3x)°$ , and $(8y-102)°$ with a total of $180°$ .

Given $a=8$ , $b=2$ , and $A=10^{\circ}$ , find if this forms 1, 2, or no triangles. Solve any triangles formed.

One angle is $66^{\circ}$ , and the third angle is $57^{\circ}$ more than half the second angle. Find the second and third angles.

Two similar triangles have sides $7x$ and $70$ for the first, and $120$ and $60$ for the second. Find $x$ .

Calculate the area of a triangle with base 10m and height 8m using $Area = \frac{1}{2} \cdot base \cdot height$ .

The diagram shows a triangle.
What is the value of $s$ ? $s=\square^{\circ}$

The diagram shows a triangle.
What is the value of $u$ ? $u=$

3. (15 pts) Given is that $A=38^{\circ}$ and $b=19 \mathrm{~cm}$ and $c=22 \mathrm{~cm}$ . Solve the triangle $A B C$ . Round measures to 1 decimal place if necessary.

Triangle $D E F$ is formed by connecting the midpoints of the side of triangle $A B C$ . The lengths of the sides of triangle $A B C$ are shown. Find the perimeter of triangle $D E F$ . Figures not necessarily drawn to scale.

Triangle $U V W$ is formed by connecting the midpoints of the side of triangle RST. The lengths of the sides of triangle $R S T$ are shown. What is the length of $\overline{W V}$ ? Figures not necessarily drawn to scale.

Which of the following sets of numbers could represent the three sides of a triangle?
Answer $\{13,25,40\}$ $\{10,16,25\}$ Submit Answer $\{6,18,25\}$ $\{13,22,35\}$

For the right triangles below, find the exact values of the side lengths $a$ and $d$ . If necessary, write your responses in simplified radical form. $a=$ $\square$ $d=$ $\square$

rieți rezolvările complete.
1. In triunghiul $A B C, A D \perp B C, D \in B C$ , iar punctele $M, N$ și $P$ sunt mijloacele laturilor $A B, A C$ , respectiv $B C$ . Demonstrați că $M N P D$ este trapez isoscel.

Triangle - Interior Angles Find the measure of the indicated angle in each triangle. 1)
21 3) $m \angle U=$ $\qquad$ $m \angle B=$ $\qquad$

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg: WI cm Length of the longer leg: $\square$ cm
Length of the hypotenuse: $\square$ cm

For the right triangles below, find the exact values of the side lengths $d$ and $c$ . If necessary, wite your responses in simplified radical form.

Find the length of side $a$ to the nearest tenth of a meter:
Law of Cosines: $a^{2}=b^{2}+c^{2}-2 b c \cdot \cos A$

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Desmos | Beautition. The National Archive. Answer Attempt 1 out of 6

6. Classify the triangle with the following side lengths: $20,21,29$

Use the Law of Sines to find the length of each side of the parallelogram. Round to the nearest tenth. a. $A B \approx$ $\qquad$ cm b. $A D \approx$ $\qquad$ cm c. $D C \approx$ $\qquad$ cm d. $B C \approx$ $\square$ type your answercm olu

Find the area of the triangle formed by the lines: $y=-2x+15$ , $y=-\frac{1}{2}x+3$ , and $y=x+3$ .

Find the length of one leg of a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle with hypotenuse $22 \sqrt{2}$ units.

Triangles $ABC$ and $DEF$ are similar. If $DEF$ has an area of 6 sq ft, find the area of $ABC$ with sides 12 ft and 4 ft.

A painter is painting a right triangle gable with sides $8' - 4"$ and $8' - 4"$ . What is the area to paint, rounded to the nearest hundredth?

A ladder leans against a wall at $60^{\circ}$ . The base is $2 \mathrm{~m}$ from the wall. Find the wall height and ladder length. $[\sin 60=0.866, \cos 60=0.5, \tan 60=1.732]$

Find $A C$ in a triangular prism where angle $B P C=90^{\circ}$ . Also, find angle $x$ if $24 \tan x=\sqrt{3}$ .

State if each triangle is acute, obtuse, or right. 3) $\begin{array}{c} 12^{2}+2^{2}=12 \mathrm{~cm} \\ 13^{2}=169 \end{array}$ 4)
Find the missing side. Round to the nearest tenth. 5) 6)

(2) Part A:
Calculate the height of the triangle to the neares! tenth of a meter. A. 10.9 m B. 12.9 m C. 15.3 m D. 16.7 m

Solve for $x$ in the triangle. Round your answer to the nearest tenth. $x=$

Question 5 of 10 Is $\triangle A B C \sim \triangle D E F$ ? If so, identify the similarity postulate or theorem that applies. A. Similar - AA B. Similar-SSS C. Similar-SAS D. Cannot be determined

Find the area of $\triangle U V W$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth. $\square$ $\mathrm{km}^{2}$

The line segment shown in the xy-plane represents one of the legs of a right triangle. The area of this triangle is $48\sqrt{13}$ square units. What is the length, in units, of the other leg of this triangle?
A 16 B 32 C $3\sqrt{13}$

Solve for x and find angle D. $x^{\circ}$ x = Angle D =

$9a-4$ A P $5a+5$ Y $6a-1$ T Find $AY$ .