Question

solve for ( x ). round to the nearest tenth of a degree,

Explanation:

Step1: Use trigonometric ratio

In a right - triangle \(ABC\) with \(\angle B = 90^{\circ}\), we know that \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is \(AB = 15\) and the hypotenuse \(AC=25\). So, \(\sin x=\frac{15}{25}\).

Step2: Simplify the ratio and find the angle

Simplify \(\frac{15}{25}=\frac{3}{5}=0.6\). Then, \(x = \sin^{- 1}(0.6)\). Using a calculator, \(x\approx36.9^{\circ}\)

Answer:

\(x\approx36.9^{\circ}\)