Question

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

Explanation:

Step1: Use the sine function

In a right - triangle, the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $x$ in right - triangle $HFG$ (right - angled at $G$), the opposite side to angle $x$ is $FG = 38$ and the hypotenuse is $HF=71$. So, $\sin x=\frac{FG}{HF}=\frac{38}{71}$.

Step2: Solve for $x$

Take the inverse sine (arcsin) of both sides. $x = \sin^{-1}(\frac{38}{71})$.
Using a calculator, $\frac{38}{71}\approx0.5352$. Then $x=\sin^{-1}(0.5352)$.
$\sin^{-1}(0.5352)\approx32.4^{\circ}$ (rounded to the nearest tenth of a degree).

Answer:

$32.4^{\circ}$