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

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 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 $x$, so $\frac{x}{\sin B}=\frac{316}{\sin C}$. Substituting the known values, we have $\frac{x}{\sin24.6^{\circ}}=\frac{316}{\sin57^{\circ}}$.

Step3: Solve for x

Cross - multiply to get $x=\frac{316\times\sin24.6^{\circ}}{\sin57^{\circ}}$. Calculate $\sin24.6^{\circ}\approx0.416$ and $\sin57^{\circ}\approx0.839$. Then $x=\frac{316\times0.416}{0.839}=\frac{131.456}{0.839}\approx156.7$.

Answer:

$156.7$