Question

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

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(OP = 5.1\) and the hypotenuse is \(OQ=8.9\). So, \(\cos x=\frac{5.1}{8.9}\).

Step2: Solve for \(x\)

Take the inverse cosine of \(\frac{5.1}{8.9}\). \(x = \cos^{-1}(\frac{5.1}{8.9})\).
Calculate \(\frac{5.1}{8.9}\approx0.573\). Then \(x=\cos^{-1}(0.573)\).
Using a calculator, \(x\approx55.0^{\circ}\).

Answer:

\(55.0^{\circ}\)