Question

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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $UVW$, we know the opposite side ($VW = 7.9$) and the hypotenuse ($UW=15$) with respect to angle $x$. We use the sine ratio $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin x=\frac{7.9}{15}$.

Step2: Solve for $x$

We take the inverse - sine of both sides: $x = \sin^{-1}(\frac{7.9}{15})$. Calculate $\frac{7.9}{15}\approx0.5267$. Then $x=\sin^{-1}(0.5267)$. Using a calculator, $x\approx31.8^{\circ}$.

Answer:

$31.8^{\circ}$