Question

use the law of sines to find the indicated side x. (assume a = 364. round your answer to two decimal places.)

Explanation:

Step1: Find angle \( C \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( C=180^{\circ}-98.4^{\circ}-24.6^{\circ}=57^{\circ} \).

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{x}{\sin B}=\frac{a}{\sin A} \). Here, \( B = 24.6^{\circ} \), \( A = 57^{\circ} \), and \( a = 364 \). So, \( x=\frac{364\times\sin24.6^{\circ}}{\sin57^{\circ}} \).
Calculate \( \sin24.6^{\circ}\approx0.416 \) and \( \sin57^{\circ}\approx0.839 \).
Then \( x=\frac{364\times0.416}{0.839}\approx180.77 \).

Answer:

\( 180.77 \)