Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, for angle $x$, the opposite side to $x$ is $GH = 3$ and the hypotenuse is $FH=4.2$. So, $\sin x=\frac{3}{4.2}$.

Step2: Solve for $x$

We know that if $\sin x = a$, then $x=\sin^{- 1}(a)$. So, $x=\sin^{-1}(\frac{3}{4.2})$.
Calculate $\frac{3}{4.2}\approx0.7143$. Then $x=\sin^{-1}(0.7143)$.
Using a calculator, $x\approx45.6^{\circ}$.

Answer:

$45.6$