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 \(73\) and the hypotenuse is \(97\). So, \(\sin x=\frac{73}{97}\).

Step2: Calculate the value of \(x\)

Take the inverse sine of \(\frac{73}{97}\). \(x = \sin^{-1}(\frac{73}{97})\). Using a calculator, \(\frac{73}{97}\approx0.7526\). Then \(x=\sin^{-1}(0.7526)\approx48.8^{\circ}\).

Answer:

\(48.8^{\circ}\)