Question

question 9 of 10
use the law of sines to find the length of side c. round your answer to the nearest tenth.

a. 44.9
b. 32.7
c. 32.0
d. 60.3

Explanation:

Step1: Find angle \( B \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( B=180^{\circ}-46.7^{\circ}-48^{\circ}=85.3^{\circ} \).

Step2: Apply the Law of Sines

The Law of Sines is \( \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \). Here, we use \( \frac{c}{\sin C}=\frac{BC}{\sin B} \). Substituting \( BC = 44 \), \( C = 46.7^{\circ} \), \( B = 85.3^{\circ} \), we get \( c=\frac{44\times\sin46.7^{\circ}}{\sin85.3^{\circ}} \).
Calculate \( \sin46.7^{\circ}\approx0.728 \), \( \sin85.3^{\circ}\approx0.996 \). Then \( c=\frac{44\times0.728}{0.996}\approx32.7 \).

Answer:

B. 32.7