Question

solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle \(x\) is defined as \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(PQ = 8.5\) and the hypotenuse is \(QO=18\). So, \(\cos x=\frac{8.5}{18}\).

Step2: Solve for \(x\)

We know that \(x = \cos^{-1}(\frac{8.5}{18})\). First, calculate \(\frac{8.5}{18}\approx0.4722\). Then, \(x=\cos^{-1}(0.4722)\). Using a calculator, \(x\approx61.8^{\circ}\).

Answer:

\(61.8\)