Math / Trigonometry

QuestionQuestion 7, 6.1.1 HW Score: 44.449 Points: 0.330
Solve the triangle. $B=74^{\circ}$ (Do not round until the final answer. Then round to the nearest degree as needed.) $\mathrm{b} \approx$ $\square$ (Do not round until the final answer. Then round to the nearest tenth as needed.) $c \approx \square$ (Do not round until the final answer. Then round to the nearest tenth as needed.)

Studdy Solution

STEP 1

1. The triangle is a non-right triangle.
2. Angle $A = 32^\circ$ , angle $B = 74^\circ$ .
3. Side $a = 9$ is opposite angle $A$ .
4. We need to find side $b$ opposite angle $B$ and side $c$ opposite angle $C$ .

STEP 2

1. Calculate the measure of angle $C$ .
2. Use the Law of Sines to find side $b$ .
3. Use the Law of Sines to find side $c$ .

STEP 3

Calculate the measure of angle $C$ using the sum of angles in a triangle:
$A + B + C = 180^\circ$ $32^\circ + 74^\circ + C = 180^\circ$ $C = 180^\circ - 32^\circ - 74^\circ$ $C = 74^\circ$

STEP 4

Use the Law of Sines to find side $b$ :
$\frac{a}{\sin A} = \frac{b}{\sin B}$ $\frac{9}{\sin 32^\circ} = \frac{b}{\sin 74^\circ}$
Solve for $b$ :
$b = \frac{9 \cdot \sin 74^\circ}{\sin 32^\circ}$
Calculate $b$ (do not round until the final answer):
$b \approx \frac{9 \cdot 0.9613}{0.5299}$ $b \approx \frac{8.6517}{0.5299}$ $b \approx 16.3$

STEP 5

Use the Law of Sines to find side $c$ :
$\frac{a}{\sin A} = \frac{c}{\sin C}$ $\frac{9}{\sin 32^\circ} = \frac{c}{\sin 74^\circ}$
Since $C = B = 74^\circ$ , the calculation is similar to side $b$ :
$c = \frac{9 \cdot \sin 74^\circ}{\sin 32^\circ}$
Calculate $c$ (do not round until the final answer):
$c \approx \frac{9 \cdot 0.9613}{0.5299}$ $c \approx \frac{8.6517}{0.5299}$ $c \approx 16.3$
The approximate lengths of the sides are: $b \approx 16.3$ $c \approx 16.3$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms