Question

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

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side to angle \(x\) is \(65\) and the hypotenuse is \(75\). So, \(\sin x=\frac{65}{75}\).

Step2: Calculate the value of \(x\)

\(x = \sin^{- 1}(\frac{65}{75})\).
\(\frac{65}{75}=\frac{13}{15}\approx0.8667\).
\(x=\sin^{-1}(0.8667)\).
Using a calculator, \(x\approx60.1^{\circ}\).

Answer:

\(60.1^{\circ}\)