Question

use the law of sines to find the indicated side x in the following figure. (round your answer to one decimal place.)

Explanation:

Step1: Find angle C

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

Step2: Apply the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. We want to find $x$, and we know that $\frac{x}{\sin B}=\frac{400}{\sin C}$. Substituting the values, we have $\frac{x}{\sin24.6^{\circ}}=\frac{400}{\sin57^{\circ}}$.

Step3: Solve for x

Cross - multiply to get $x=\frac{400\times\sin24.6^{\circ}}{\sin57^{\circ}}$. Calculate $\sin24.6^{\circ}\approx0.416$ and $\sin57^{\circ}\approx0.839$. Then $x=\frac{400\times0.416}{0.839}=\frac{166.4}{0.839}\approx198.3$.

Answer:

$198.3$