Question

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

Explanation:

Step1: Identify trigonometric ratio

Since we know the opposite side ($HG = 7.4$) and the hypotenuse ($FH=12$) with respect to angle $x$, we use the sine - ratio $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin x=\frac{7.4}{12}$.

Step2: Calculate the value of $\sin x$

$\sin x=\frac{7.4}{12}\approx0.6167$.

Step3: Find the value of $x$

We know that $x = \sin^{- 1}(0.6167)$. Using a calculator, $x=\sin^{-1}(0.6167)\approx38.0^{\circ}$.

Answer:

$38.0^{\circ}$