Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Use sine function

In right - triangle RST, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 38^{\circ}$, the opposite side to $\angle T$ is $RS = 99$ and the hypotenuse is $x$. So, $\sin38^{\circ}=\frac{99}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{99}{\sin38^{\circ}}$. Since $\sin38^{\circ}\approx0.6157$, then $x=\frac{99}{0.6157}\approx160.8$.

Answer:

$160.8$