Triangles

Problem 301

From $A$ to $B$ a private plane flies 1.5 hours at 110 mph on a bearing of $29^{\circ}$ . It turns at point $B$ and continues another 2.2 hours at the same speed, but on a bearing of $119^{\circ}$ to point $C$ . Round each answer to three decimal places.
At the end of this time, how far is the plane from its starting point? $\square$ miles
On what bearing is the plane from its original location? $\square$ degrees

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Problem 302

Find the perimeter of triangle ABC where $AF=6$ , $CD=5$ , and $BE=4$ .

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Problem 303

Un voilier a un mât de $3,6 \mathrm{~m}$ avec un étai de $4,2 \mathrm{~m}$ et des haubans de $3,9 \mathrm{~m}$ . Est-ce que les triangles VEN et VNT sont rectangles ? Justifie.

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Problem 304

Find the length of the third side of a triangle with sides 30.3 m, 18.5 m, and an angle of $61^{\circ}$ between them.

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Problem 305

Find the third side of a triangle with sides 30.3 m and 18.5 m, and an angle of $61^{\circ}$ . Options: 24.1 m, 26.8 m, 30.0 m, 32.6 m.

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Problem 306

Find the length of the third side of a triangle with sides $600 \mathrm{~m}$ , $250 \mathrm{~m}$ , and opposite angle $34^{\circ}$ .

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Problem 307

Find the length of the third side of a triangle with sides $45.3 \mathrm{~m}$ , $29.0 \mathrm{~m}$ , and angle $26^{\circ}$ .

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Problem 308

Find the area of triangle formed by points A(3,5), B(7,5), and C(7,-1).

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Problem 309

In a coordinate plane, $\triangle ABC$ is a right triangle with $A(-4,1)$ and $B(2,1)$ . Area is 9 sq. units. Find point $C$ .

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Problem 310

In a coordinate plane, $\triangle ABC$ has $A(-4,1)$ and $B(2,1)$ with area 9 sq. units. Find other $C$ coordinates besides $(2,4)$ .

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Problem 311

In triangle ABC, DE and FG are parallel to CB. Given AE = 9, EG = 8, GB = 7, find the length of AC in inches.

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Problem 312

Triangle $ABC$ has an area of $108 \, \text{cm}^2$ . If base $x$ and height $y$ are integers, find possible values for $x$ . Choices: (A) 4, (B) 5, (C) 6, (D) 8, (E) 9.

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Problem 313

In a triangle, if side $x = \frac{3}{5} z$ and $y = \frac{4}{3} x$ , find the ratio of $y$ to $z$ .

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Problem 314

A right triangle has an area of 16 square miles. One leg is 4 miles longer than the other. Find the leg lengths. $b(b+4)=32$ $\frac{1}{2} \times b \times h=16$

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Problem 315

A right triangle has an area of 16 square miles. One leg is 4 miles longer than the other. Find the leg lengths.

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Problem 316

Find the height of a scalene triangle with base $b = 4$ units and area $A = 16$ square units.

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Problem 317

Find the base of a triangle with height $12 \mathrm{~cm}$ more than base and area $32 \mathrm{~cm}^{2}$ . Options: A. $4 \mathrm{~cm}$ B. $8 \mathrm{~cm}$ C. $12 \mathrm{~cm}$ D. $16 \mathrm{~cm}$

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Problem 318

Three charges of $+6.65 \mu \mathrm{C}$ at the triangle's vertices create a force. Find the resultant force: a. $172.34 \mathrm{~N}$ b. $22.98 \mathrm{~N}$ c. $34.47 \mathrm{~N}$ d. $68.94 \mathrm{~N}$ e. $0.89 \mathrm{~N}$

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Problem 319

Find angle $B$ in triangle $ABC$ if $A=15^{\circ}$ and $C=50^{\circ}$ .

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Problem 320

Find the perimeter of triangle PQR with vertices at $P(-10,-2)$ , $Q(-10,6)$ , and $R(5,2)$ .

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Problem 321

Find the perimeter of triangle PQR with vertices at $P(-10,-2)$ , $Q(-10,6)$ , and $R(5,2)$ .

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Problem 322

Find the area of the triangle with vertices $(4,4)$ , $(4,0)$ , and $(0,0)$ by counting whole and half squares. 8 sq. units. Which quadrant is the point $(-3,2)$ in? Second.

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Problem 323

Prove that $c^{2}=a^{2}+b^{2}-2ab\cos C$ .

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Problem 324

Triunghiul echilateral $ABC$ are perimetrul $27 \mathrm{~cm}$ . Găsește lungimea segmentului $MC$ , unde $AN=6 \mathrm{~cm}$ .

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Problem 325

Найдите периметр равнобедренного треугольника, если одна сторона $a = 7$ дм, а другая $b = a + 8$ дм.

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Problem 326

Una gaviota observa un bote a $42^{\circ}$ de depresión desde 45 m de altura. ¿Cuál es la distancia horizontal al barco?

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Problem 327

Desde una torre de 28 m, un salvavidas ve a una persona con un ángulo de depresión de $58^{\circ}$ . ¿Cuál es la distancia a la persona?

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Problem 328

已知圆O的半径为2.5，弦AB的长度为2，若三角形ABC为等腰三角形，则求 $BC^{2}=$ 。

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Problem 329

Calculați aria triunghiului $B O D$ și măsura unghiului $B A D$ în patrulaterul convex $A B C D$ cu datele date.

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Problem 330

4. Într-un pătrat $A B C D$ , cu punctele $E, F, G$ pe laturi, arată că triunghiul $D E G$ este isoscel și află unghiul dintre $D F$ și $E G$ .

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Problem 331

5. Într-un dreptunghi cu $AB=12 \mathrm{~cm}$ și $BC=4 \mathrm{~cm}$ , calculează aria triunghiului $CEO$ și unghiul $BFC$ .

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Problem 332

Un topógrafo mide el ángulo de elevación al cerro: $45^{\circ}$ y a $800$ m más, $30^{\circ}$ . ¿Cuál es la altura del cerro?

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Problem 333

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5 \text{ km}$ , $AC=1.2 \text{ km}$ , and $\angle A=50^\circ$ .

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Problem 334

等腰三角形一个底角为 45 度，问这个三角形的类型是？(1) 锐角 (2) 直角 (3) 钝角 (4) 无法确定

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Problem 335

1. Într-o livadă sunt 160 de pomi. În prima zi s-au plantat $60\%$ meri și $40\%$ nuci, iar în a doua zi 76 pomi. Află procentul din prima zi și câți meri și nuci s-au plantat.
2. Consideră $E(x)=x^{2}-(x+1)^{2}-(x+2)^{2}+(x+3)^{2}$ . Arată că $E(x)=4$ pentru orice $x$ și calculează suma $S=1^{2}-2^{2}-3^{2}+4^{2}+\ldots+40^{2}$ .
3. În sistemul de axe $x O y$ , $A(3,2)$ , $B$ simetricul lui $A$ față de $O x$ , și $C$ simetricul lui $A$ față de $O$ . Arată că $C=(-3,-2)$ și determină funcția corespunzătoare lui $BC$ .
4. Semicercul de centru $D$ este tangent la laturile $A B$ și $A C$ ale triunghiului isoscel $A B C$ . Demonstrează că $D$ este mijlocul lui $B C$ și află raza semicercului, știind că $B C=30 \mathrm{~cm}$ și $A D=20 \mathrm{~cm}$ .

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Problem 336

Find the perimeter of triangle $ABC$ with $AD=4 \sqrt{3} cm$ , $BC=5 cm$ , and $BD=1 cm$ .

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Problem 337

Find the circumcenter of $\triangle E F G$ with $E(4,4), F(4,2)$ , and $G(8,2)$ . Hint: Draw a picture
Select one: A. $(6,3)$ B. $(4,2)$ C. $(4,4)$ D. $(3,6)$

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Problem 338

EXERCICE 4 Ce n'est pas une figure en vraie grandeur. On donne: - Les points K, O, L sont alignés ; O est entre K et $\mathrm{L} ; \mathrm{OK}=2 \mathrm{~cm}$ ; $\mathrm{OL}=3,6 \mathrm{~cm}$ . - Les points J, O, N sont alignés ; $O$ est entre $J$ et $N ; O J=3 \mathrm{~cm}$ ; - Les triangles OKJ et OLN sont rectangle en $K$ et $L$ .
1. Démontrer que les droites (JK) et (LN) sont parallèles.
2. Calculer JK.
3. Calculer ON.

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Problem 339

Find the measures triangle 3)
Find the meas

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Problem 340

Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. III only C. I or III only D. I, II, or II
Select one: A. A B. $B$ C. C D. $D$

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Problem 341

Is it possible for a triangle to have sides with the given lengths? Explain. 5 in., 8 in., 15 in. A. Yes; the sum of each pair is greater than the third. B. No; $5+8$ is not greater than 15 . C. $\mathrm{No} ; 15^{2}>5^{2}+8^{2}$ . D. Yes; $15^{2}>5^{2}+8^{2}$ .

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Problem 342

Exercice $\mathrm{n}^{\circ} 3:(8 \mathrm{pts})$ Soit ABC un triangle tel que : $\mathrm{AB}=4 ; \mathrm{AC}=6$ et $\mathrm{BC}=8$ . Soit $M$ un point du segment $[\mathrm{AB}]$ tel que $\mathrm{AM}=1$ . 1) a/ Faites une figure. b/ Construire le point N du segment [AC] tel que $A N=\frac{1}{4} \mathrm{AC}$ . c/ Montrer que les droites (MN) et (BC) sont parallèles. d/ Montrer que MN $=2$ . 2) Les droites (MC) et ( BN ) se coupent en I et la parallèle à (BC) passant par I co (AB) en J. a/ Montrer que $\frac{\mathrm{IJ}}{\mathrm{MN}}=\frac{\mathrm{BI}_{\mathrm{II}}}{\mathrm{BM}_{\mathrm{II}}}$ puis $\frac{\mathrm{II}}{\mathrm{BC}}=\frac{\mathrm{MI}}{\mathrm{MB}}$ . b/ En déduire que $\frac{\mathrm{IJ}}{\mathbf{M N}}+\frac{\mathrm{IJ}}{\mathbf{B C}}=1$ . c/ Calculer alors IJ puis MJ.

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Problem 343

B) Solve. 11) In \triangle A B C, m \Varangle A=-7 x+1, m \Varangle B=-x+13, and m \Varangle C=-2 x-4. Draw and label of the triangle. a) Solve for $x$ and the measures of the angles. \begin{array}{l} x= \\ m \Varangle A= \\ m \Varangle B= \\ m \Varangle C= \end{array} b) Order the sides from least to greatest.
ANSWER: $\qquad$ $<$ $\qquad$

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Problem 344

Übung 22 Gegeben ist ein Dreieck ABC mit $\mathrm{A}(1 \mid 2), \mathrm{B}(9 \mid 0)$ und $\mathrm{C}(5 \mid 6)$ . a) Stellen Sie Parametergleichungen der Mittelsenkrechten $g_{A B}$ und $g_{A C}$ auf. b) Berechnen Sie den Schnittpunkt der Mittelsenkrechten $g_{A B}$ und $g_{A C}$ . c) Stellen Sie das Dreieck $A B C$ sowie die Mittelsenkrechten $g_{A B}$ und $g_{A C}$ zeichnerisch dar.

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Problem 345

he perimeter. Simplify your answer.

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Problem 346

Name: $\qquad$ Use this diagram to answer the following questions. $\qquad$ 6. In the above diagram, what is the length of side $X Z$ ? a. 4.8 cm b. 8.3 cm c. 16.4 cm d. 23.0 cm $\qquad$ 7. In the above diagram, what is the measure of $\angle X$ ? a. $37.6^{\circ}$ b. $39.7^{\circ}$ c. $50.2^{\circ}$ d. $52.4^{\circ}$ $\qquad$ 8. In the above diagram, what is the measure of $\angle Z$ ? a. $37.6^{\circ}$ b. $39.7^{\circ}$ c. $50.2^{\circ}$ d. $52.4^{\circ}$

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Problem 347

Considera le due funzioni: $f(x)=|x-2|-1 \quad \text { e } g(x)=-\frac{1}{2} x+2$ a. Traccia i loro grafici e determina l'area del triangolo che essi individuano. b. Risolvi graficamente la disequazione $f(x) \geq g(x)$ .

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Problem 348

Suppose that $\triangle Q R S$ is isosceles with base $\overline{S Q}$ . Suppose also that $m \angle S=(3 x+19)^{\circ}$ and $m \angle Q=(5 x-9)^{\circ}$ . Find the degree measure of each angle in the triangle. $\begin{array}{l} m \angle Q=\square^{\circ} \\ m \angle R=\square^{\circ} \\ m \angle S=\square^{\circ} \end{array}$

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Problem 349

The longer leg of a right triangle is 7 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: $\square$ cm
Length of the longer leg: $\square$ cm
Length of the hypotenuse: $\square$ cm

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Problem 350

For the following right triangle, find the side length $x$ .

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Problem 351

A kite flying in the air has a 12-ft line attached to it. Its line is pulled taut and casts an $11-\mathrm{ft}$ shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth. $\square$ ft

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Problem 352

LEVEL: 1/1 7 more questions to go AFTER LEVEL: 1
Given that point G is the incenter of $\triangle H J K$ , which of the following is true? $G F=E G$ $G J=E G$ $H E=E K$ Two of these Submit Porents Feedbock Questions? About Careers Terms of Service PRIVACY POLICY Contact Us Desk 1

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Problem 353

4. $\qquad$ $\angle J=$ $\qquad$ $\angle K=$ $\qquad$ $\angle \mathrm{L}=$ $\qquad$

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Problem 354

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Problem 355

Area of shaded region $=24$ in $^{2}$ $t=$ $\square$ inches

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Problem 356

Classify this triangle by its sides and angle

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Problem 357

The two triangle shown below are similar triangles.
What is the value of $d$ in meters?

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Problem 358

Solve for x .

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Problem 359

Solve for x .

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Problem 360

What is the area of the triangle? $\square$ square units

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Problem 361

Find the value of $x$ .

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Problem 362

Find the value of $x$ .

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Problem 363

Solve the triangle. $a=63, b=22, c=48$ $A \approx$ $\square$ $B \approx$ $\square$ ${ }^{\circ}$ $C \approx 40^{\circ}$ (Do not round until the final answer. Then round to the nearest degree as needed.)

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Problem 364

What is the perimeter? If necessary, round to the nearest tenth. $\square$ centimeters

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Problem 365

Solve the right triangle. 40.

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Problem 366

What is the perimeter? If necessary, round to the nearest tenth. $\square$ centimeters

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Problem 367

41.

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Problem 368

What is the perimeter? If necessary, round to the nearest tenth. $\square$ inches

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Problem 369

**Solve for all missing sides and angles in the triangle below:

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Problem 370

Solving a word problem
Mountain officials want to build a new ski lift from $B$ to $C$ , as shown in the figure below. The distance from $A$ to $C$ is 1490 feet. They measure angle $D A C$ to be $35^{\circ}$ and angle $D B C$ to be $21^{\circ}$ . What is the distance from $A$ to $B$ ? Round your answer to the nearest tenth of a foot. $\square$ feet

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Problem 371

28. Use the figure to answer questions $a$ and $b$ . a. Are the triangles above similar? Explain. b. If possible, find the missing side length, $x$ .

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Problem 372

8.

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Problem 373

Find $D F$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth.

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Problem 374

Find $W Y$ .
Write your answer in simplified, rationalized form. Do not round.

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Problem 375

Find QS.
Write your answer as an integer or as a decimal rounded to the nearest tenth. $Q S=$ $\square$

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Problem 376

Find the expression for the area of a triangular attic floor with height $n \mathrm{yd}$ and base $6 \mathrm{yd}$ .

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Problem 377

삼각형의 변이 $x-1, x, x+1$ 일 때, $x$ 의 가능한 값 중 아닌 것은? (1) 2 (2) 3 (3) 4 (4) 5 (5) 6

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Problem 378

Calcola perimetro e area di un triangolo rettangolo con cateti di $10 \mathrm{~cm}$ e $24 \mathrm{~cm}$ .

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Problem 379

Calcola perimetro e area di un triangolo rettangolo con ipotenusa $75 \mathrm{~cm}$ e cateto $45 \mathrm{~cm}$ .

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Problem 380

Calcola il perimetro e l'area di un triangolo rettangolo con ipotenusa $75 \mathrm{~cm}$ e cateto $45 \mathrm{~cm}$ .

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Problem 381

Un triangolo rettangolo ha area $180 \mathrm{~cm}^{2}$ e un cateto di $9 \mathrm{~cm}$ . Trova il perimetro.

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Problem 382

Berechne die fehlende Kathetenlänge $b$ eines rechtwinkligen Dreiecks mit Fläche $A=490mm^2$ und Kathete $a=28mm$ .

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Problem 383

Gegeben sind $A=5 \, \text{cm}^{2}$ , $a=80 \, \text{mm}$ und $\gamma=90^{\circ}$ . Welche geometrische Figur ist gefragt?

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Problem 384

Berechne die fehlende Kathetenlänge eines rechtwinkligen Dreiecks mit $\gamma=90^{\circ}$ , Fläche 5 cm $^2$ und Kathete 80 mm.

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Problem 385

Bài 1. Cho tam giác vuông $\mathrm{ABC}$ với $\mathrm{AB}=30 \mathrm{~cm}$ , cao $\mathrm{AH}=24 \mathrm{cm}$ . Tính $\mathrm{BH}, \mathrm{BC}, \mathrm{AC}$ và độ dài $\mathrm{HD}$ với $\mathrm{HD} \perp \mathrm{AC}$ .

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Problem 386

Un triangolo isoscele ha base $32 \mathrm{~cm}$ e altezza $12 \mathrm{~cm}$ . Trova perimetro e area.

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Problem 387

Calcola l'area di un triangolo isoscele con perimetro $36 \mathrm{~cm}$ e lato obliquo $13 \mathrm{~cm}$ .

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Problem 388

Diberi $AB = AC$ dan kecerunan $AB = \frac{2}{3}$ . Jika $BC = 12$ cm, cari tinggi $A$ dari $BC$ .

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Problem 389

Find the area of a triangle with a chord of length $10 \mathrm{~cm}$ in a circle of radius $13 \mathrm{~cm}$ .

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Problem 390

In un triangolo rettangolo, i cateti sommano a $21 \mathrm{~cm}$ e differiscono di $3 \mathrm{~cm}$ . Trova l'altezza sull'ipotenusa di $15 \mathrm{~cm}$ .

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Problem 391

In un triangolo rettangolo, i cateti sommano a $21 \mathrm{~cm}$ e differiscono di $3 \mathrm{~cm}$ . Trova l'altezza sull'ipotenusa di $15 \mathrm{~cm}$ .

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Problem 392

Calcola il perimetro di un triangolo isoscele con area di $672 \mathrm{~cm}^{2}$ e base di $28 \mathrm{~cm}$ .

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Problem 393

Un triangolo ha area $14,95 \mathrm{~cm}^{2}$ e un cateto di $6,5 \mathrm{~cm}$ . Trova l'altro cateto e l'altezza sull'ipotenusa di $13 \mathrm{~cm}$ .

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Problem 394

In un triangolo rettangolo, un cateto è $36 \mathrm{~cm}$ e l'altro è $\frac{4}{3}$ volte il primo. Trova perimetro e area.

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Problem 395

Bài 1. Cho tam giác $ABC$ vuông tại $A$ với $\mathrm{AB}=30 \mathrm{~cm}$ , cao $\mathrm{AH}=24 \mathrm{cm}$ . Tính $BH$ , $BC$ , $AC$ và $HD$ .

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Problem 396

A triangle has sides of 6 in and 26 in. Find the area of a similar triangle with sides half the length of the original.

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Problem 397

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5$ km, $AC=1.2$ km, and $\hat{A}=50^{\circ}$ .

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Problem 398

In un triangolo rettangolo, i cateti sommano a $21 \mathrm{~cm}$ e differiscono di $3 \mathrm{~cm}$ . Trova l'altezza sull'ipotenusa di $15 \mathrm{~cm}$ .

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Problem 399

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5$ km, $AC=1.2$ km, and $\hat{A}=50^\circ$ .

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Problem 400

A surveyor sees a building at $34^{\circ}$ elevation, 2544 ft away. Find distance to the building, building height, antenna angle, and height.

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1 2 3 4 5 6 7 ...10

Triangles

Problem 301

Problem 302

Find the perimeter of triangle ABC where AF=6AF=6AF=6, CD=5CD=5CD=5, and BE=4BE=4BE=4.

Problem 303

Un voilier a un mât de 3,6 m3,6 \mathrm{~m}3,6 m avec un étai de 4,2 m4,2 \mathrm{~m}4,2 m et des haubans de 3,9 m3,9 \mathrm{~m}3,9 m. Est-ce que les triangles VEN et VNT sont rectangles ? Justifie.

Problem 304

Find the length of the third side of a triangle with sides 30.3 m, 18.5 m, and an angle of 61∘61^{\circ}61∘ between them.

Problem 305

Find the third side of a triangle with sides 30.3 m and 18.5 m, and an angle of 61∘61^{\circ}61∘. Options: 24.1 m, 26.8 m, 30.0 m, 32.6 m.

Problem 306

Find the length of the third side of a triangle with sides 600 m600 \mathrm{~m}600 m, 250 m250 \mathrm{~m}250 m, and opposite angle 34∘34^{\circ}34∘.

Problem 307

Find the length of the third side of a triangle with sides 45.3 m45.3 \mathrm{~m}45.3 m, 29.0 m29.0 \mathrm{~m}29.0 m, and angle 26∘26^{\circ}26∘.

Problem 308

Find the area of triangle formed by points A(3,5), B(7,5), and C(7,-1).

Problem 309

In a coordinate plane, △ABC\triangle ABC△ABC is a right triangle with A(−4,1)A(-4,1)A(−4,1) and B(2,1)B(2,1)B(2,1). Area is 9 sq. units. Find point CCC.

Problem 310

In a coordinate plane, △ABC\triangle ABC△ABC has A(−4,1)A(-4,1)A(−4,1) and B(2,1)B(2,1)B(2,1) with area 9 sq. units. Find other CCC coordinates besides (2,4)(2,4)(2,4).

Problem 311

In triangle ABC, DE and FG are parallel to CB. Given AE = 9, EG = 8, GB = 7, find the length of AC in inches.

Problem 312

Triangle ABCABCABC has an area of 108 cm2108 \, \text{cm}^2108cm2. If base xxx and height yyy are integers, find possible values for xxx. Choices: (A) 4, (B) 5, (C) 6, (D) 8, (E) 9.

Problem 313

In a triangle, if side x=35zx = \frac{3}{5} zx=53​z and y=43xy = \frac{4}{3} xy=34​x, find the ratio of yyy to zzz.

Problem 314

A right triangle has an area of 16 square miles. One leg is 4 miles longer than the other. Find the leg lengths. b(b+4)=32 b(b+4)=32 b(b+4)=32 12×b×h=16 \frac{1}{2} \times b \times h=16 21​×b×h=16

Problem 315

A right triangle has an area of 16 square miles. One leg is 4 miles longer than the other. Find the leg lengths.

Problem 316

Find the height of a scalene triangle with base b=4b = 4b=4 units and area A=16A = 16A=16 square units.

Problem 317

Find the base of a triangle with height 12 cm12 \mathrm{~cm}12 cm more than base and area 32 cm232 \mathrm{~cm}^{2}32 cm2. Options: A. 4 cm4 \mathrm{~cm}4 cm B. 8 cm8 \mathrm{~cm}8 cm C. 12 cm12 \mathrm{~cm}12 cm D. 16 cm16 \mathrm{~cm}16 cm

Problem 318

Three charges of +6.65μC+6.65 \mu \mathrm{C}+6.65μC at the triangle's vertices create a force. Find the resultant force: a. 172.34 N172.34 \mathrm{~N}172.34 N b. 22.98 N22.98 \mathrm{~N}22.98 N c. 34.47 N34.47 \mathrm{~N}34.47 N d. 68.94 N68.94 \mathrm{~N}68.94 N e. 0.89 N0.89 \mathrm{~N}0.89 N

Problem 319

Find angle BBB in triangle ABCABCABC if A=15∘A=15^{\circ}A=15∘ and C=50∘C=50^{\circ}C=50∘.

Problem 320

Find the perimeter of triangle PQR with vertices at P(−10,−2)P(-10,-2)P(−10,−2), Q(−10,6)Q(-10,6)Q(−10,6), and R(5,2)R(5,2)R(5,2).

Problem 321

Find the perimeter of triangle PQR with vertices at P(−10,−2)P(-10,-2)P(−10,−2), Q(−10,6)Q(-10,6)Q(−10,6), and R(5,2)R(5,2)R(5,2).

Problem 322

Find the area of the triangle with vertices (4,4)(4,4)(4,4), (4,0)(4,0)(4,0), and (0,0)(0,0)(0,0) by counting whole and half squares. 8 sq. units. Which quadrant is the point (−3,2)(-3,2)(−3,2) in? Second.

Problem 323

Prove that c2=a2+b2−2abcos⁡Cc^{2}=a^{2}+b^{2}-2ab\cos Cc2=a2+b2−2abcosC.

Problem 324

Triunghiul echilateral ABCABCABC are perimetrul 27 cm27 \mathrm{~cm}27 cm. Găsește lungimea segmentului MCMCMC, unde AN=6 cmAN=6 \mathrm{~cm}AN=6 cm.

Problem 325

Найдите периметр равнобедренного треугольника, если одна сторона a=7a = 7a=7 дм, а другая b=a+8b = a + 8b=a+8 дм.

Problem 326

Una gaviota observa un bote a 42∘42^{\circ}42∘ de depresión desde 45 m de altura. ¿Cuál es la distancia horizontal al barco?

Problem 327

Desde una torre de 28 m, un salvavidas ve a una persona con un ángulo de depresión de 58∘58^{\circ}58∘. ¿Cuál es la distancia a la persona?

Problem 328

已知圆O的半径为2.5，弦AB的长度为2，若三角形ABC为等腰三角形，则求BC2=BC^{2}=BC2=。

Problem 329

Calculați aria triunghiului BODB O DBOD și măsura unghiului BADB A DBAD în patrulaterul convex ABCDA B C DABCD cu datele date.

Problem 330

4. Într-un pătrat ABCDA B C DABCD, cu punctele E,F,GE, F, GE,F,G pe laturi, arată că triunghiul DEGD E GDEG este isoscel și află unghiul dintre DFD FDF și EGE GEG.

Problem 331

5. Într-un dreptunghi cu AB=12 cmAB=12 \mathrm{~cm}AB=12 cm și BC=4 cmBC=4 \mathrm{~cm}BC=4 cm, calculează aria triunghiului CEOCEOCEO și unghiul BFCBFCBFC.

Problem 332

Un topógrafo mide el ángulo de elevación al cerro: 45∘45^{\circ}45∘ y a 800800800 m más, 30∘30^{\circ}30∘. ¿Cuál es la altura del cerro?

Problem 333

Calculate the distance BCBCBC in triangle ABCABCABC where AB=1.5 kmAB=1.5 \text{ km}AB=1.5 km, AC=1.2 kmAC=1.2 \text{ km}AC=1.2 km, and ∠A=50∘\angle A=50^\circ∠A=50∘.

Problem 334

等腰三角形一个底角为 45 度，问这个三角形的类型是？(1) 锐角 (2) 直角 (3) 钝角 (4) 无法确定

Problem 335

Problem 336

Find the perimeter of triangle ABCABCABC with AD=43cmAD=4 \sqrt{3} cmAD=43​cm, BC=5cmBC=5 cmBC=5cm, and BD=1cmBD=1 cmBD=1cm.

Problem 337

Find the circumcenter of △EFG\triangle E F G△EFG with E(4,4),F(4,2)E(4,4), F(4,2)E(4,4),F(4,2), and G(8,2)G(8,2)G(8,2). Hint: Draw a pictureSelect one: A. (6,3)(6,3)(6,3) B. (4,2)(4,2)(4,2) C. (4,4)(4,4)(4,4) D. (3,6)(3,6)(3,6)

Problem 338

Problem 339

Find the measures triangle 3)Find the meas

Problem 340

Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. III only C. I or III only D. I, II, or IISelect one: A. A B. BBB C. C D. DDD

Problem 341

Problem 342

Find the perimeter of triangle ABC where $AF=6$ , $CD=5$ , and $BE=4$ .

Un voilier a un mât de $3,6 \mathrm{~m}$ avec un étai de $4,2 \mathrm{~m}$ et des haubans de $3,9 \mathrm{~m}$ . Est-ce que les triangles VEN et VNT sont rectangles ? Justifie.

Find the length of the third side of a triangle with sides 30.3 m, 18.5 m, and an angle of $61^{\circ}$ between them.

Find the third side of a triangle with sides 30.3 m and 18.5 m, and an angle of $61^{\circ}$ . Options: 24.1 m, 26.8 m, 30.0 m, 32.6 m.

Find the length of the third side of a triangle with sides $600 \mathrm{~m}$ , $250 \mathrm{~m}$ , and opposite angle $34^{\circ}$ .

Find the length of the third side of a triangle with sides $45.3 \mathrm{~m}$ , $29.0 \mathrm{~m}$ , and angle $26^{\circ}$ .

In a coordinate plane, $\triangle ABC$ is a right triangle with $A(-4,1)$ and $B(2,1)$ . Area is 9 sq. units. Find point $C$ .

In a coordinate plane, $\triangle ABC$ has $A(-4,1)$ and $B(2,1)$ with area 9 sq. units. Find other $C$ coordinates besides $(2,4)$ .

Triangle $ABC$ has an area of $108 \, \text{cm}^2$ . If base $x$ and height $y$ are integers, find possible values for $x$ . Choices: (A) 4, (B) 5, (C) 6, (D) 8, (E) 9.

In a triangle, if side $x = \frac{3}{5} z$ and $y = \frac{4}{3} x$ , find the ratio of $y$ to $z$ .

A right triangle has an area of 16 square miles. One leg is 4 miles longer than the other. Find the leg lengths. $b(b+4)=32$ $\frac{1}{2} \times b \times h=16$

Find the height of a scalene triangle with base $b = 4$ units and area $A = 16$ square units.

Find the base of a triangle with height $12 \mathrm{~cm}$ more than base and area $32 \mathrm{~cm}^{2}$ . Options: A. $4 \mathrm{~cm}$ B. $8 \mathrm{~cm}$ C. $12 \mathrm{~cm}$ D. $16 \mathrm{~cm}$

Three charges of $+6.65 \mu \mathrm{C}$ at the triangle's vertices create a force. Find the resultant force: a. $172.34 \mathrm{~N}$ b. $22.98 \mathrm{~N}$ c. $34.47 \mathrm{~N}$ d. $68.94 \mathrm{~N}$ e. $0.89 \mathrm{~N}$

Find angle $B$ in triangle $ABC$ if $A=15^{\circ}$ and $C=50^{\circ}$ .

Find the perimeter of triangle PQR with vertices at $P(-10,-2)$ , $Q(-10,6)$ , and $R(5,2)$ .

Find the perimeter of triangle PQR with vertices at $P(-10,-2)$ , $Q(-10,6)$ , and $R(5,2)$ .

Find the area of the triangle with vertices $(4,4)$ , $(4,0)$ , and $(0,0)$ by counting whole and half squares. 8 sq. units. Which quadrant is the point $(-3,2)$ in? Second.

Prove that $c^{2}=a^{2}+b^{2}-2ab\cos C$ .

Triunghiul echilateral $ABC$ are perimetrul $27 \mathrm{~cm}$ . Găsește lungimea segmentului $MC$ , unde $AN=6 \mathrm{~cm}$ .

Найдите периметр равнобедренного треугольника, если одна сторона $a = 7$ дм, а другая $b = a + 8$ дм.

Una gaviota observa un bote a $42^{\circ}$ de depresión desde 45 m de altura. ¿Cuál es la distancia horizontal al barco?

Desde una torre de 28 m, un salvavidas ve a una persona con un ángulo de depresión de $58^{\circ}$ . ¿Cuál es la distancia a la persona?

已知圆O的半径为2.5，弦AB的长度为2，若三角形ABC为等腰三角形，则求 $BC^{2}=$ 。

Calculați aria triunghiului $B O D$ și măsura unghiului $B A D$ în patrulaterul convex $A B C D$ cu datele date.

4. Într-un pătrat $A B C D$ , cu punctele $E, F, G$ pe laturi, arată că triunghiul $D E G$ este isoscel și află unghiul dintre $D F$ și $E G$ .

5. Într-un dreptunghi cu $AB=12 \mathrm{~cm}$ și $BC=4 \mathrm{~cm}$ , calculează aria triunghiului $CEO$ și unghiul $BFC$ .

Un topógrafo mide el ángulo de elevación al cerro: $45^{\circ}$ y a $800$ m más, $30^{\circ}$ . ¿Cuál es la altura del cerro?

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5 \text{ km}$ , $AC=1.2 \text{ km}$ , and $\angle A=50^\circ$ .

Find the perimeter of triangle $ABC$ with $AD=4 \sqrt{3} cm$ , $BC=5 cm$ , and $BD=1 cm$ .

Find the circumcenter of $\triangle E F G$ with $E(4,4), F(4,2)$ , and $G(8,2)$ . Hint: Draw a picture
Select one: A. $(6,3)$ B. $(4,2)$ C. $(4,4)$ D. $(3,6)$

Find the measures triangle 3)
Find the meas

Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. III only C. I or III only D. I, II, or II
Select one: A. A B. $B$ C. C D. $D$

The longer leg of a right triangle is 7 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: $\square$ cm
Length of the longer leg: $\square$ cm
Length of the hypotenuse: $\square$ cm

For the following right triangle, find the side length $x$ .

A kite flying in the air has a 12-ft line attached to it. Its line is pulled taut and casts an $11-\mathrm{ft}$ shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth. $\square$ ft

4. $\qquad$ $\angle J=$ $\qquad$ $\angle K=$ $\qquad$ $\angle \mathrm{L}=$ $\qquad$

Area of shaded region $=24$ in $^{2}$ $t=$ $\square$ inches

The two triangle shown below are similar triangles.
What is the value of $d$ in meters?

What is the area of the triangle? $\square$ square units

Find the value of $x$ .

Find the value of $x$ .

Solve the triangle. $a=63, b=22, c=48$ $A \approx$ $\square$ $B \approx$ $\square$ ${ }^{\circ}$ $C \approx 40^{\circ}$ (Do not round until the final answer. Then round to the nearest degree as needed.)

What is the perimeter? If necessary, round to the nearest tenth. $\square$ centimeters

What is the perimeter? If necessary, round to the nearest tenth. $\square$ centimeters

What is the perimeter? If necessary, round to the nearest tenth. $\square$ inches

28. Use the figure to answer questions $a$ and $b$ . a. Are the triangles above similar? Explain. b. If possible, find the missing side length, $x$ .

Find $D F$ .
Write your answer as an integer or as a decimal rounded to the nearest tenth.

Find $W Y$ .
Write your answer in simplified, rationalized form. Do not round.