Question

find the measure of x. round to the nearest hundredth.

Explanation:

Step1: Identify trigonometric relation

We use the sine function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here $\theta = 38^{\circ}$, the opposite side to the $38^{\circ}$ angle is 16 and the hypotenuse is $x$. So $\sin38^{\circ}=\frac{16}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{16}{\sin38^{\circ}}$.
Since $\sin38^{\circ}\approx 0.6157$, then $x=\frac{16}{0.6157}\approx 25.99$.

Answer:

$25.99$