Question

find x. round your answer to the nearest tenth of a degree.
x = □°

Explanation:

Step1: Recall the sine function

In a right - triangle, the sine of an angle \(x\) is defined as \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side to angle \(x\) is \(5\) and the hypotenuse is \(8\). So, \(\sin x=\frac{5}{8}\).

Step2: Solve for \(x\)

To find \(x\), we use the inverse sine function \(x = \sin^{-1}(\frac{5}{8})\).
Using a calculator, \(x=\sin^{-1}(0.625)\approx38.7^{\circ}\)

Answer:

\(38.7\)