Question

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

Explanation:

Step1: Recall 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 $FGH$, the side opposite to angle $x$ is $FG = 38$, and the hypotenuse is $FH=71$. So, $\sin x=\frac{38}{71}$.

Step2: Solve for $x$

Take the inverse sine (arcsin) of both sides. $x=\sin^{- 1}(\frac{38}{71})$. Using a calculator, $\frac{38}{71}\approx0.535211$. Then $x=\sin^{-1}(0.535211)$.

Answer:

$x\approx32.4^{\circ}$