Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(OPQ\), we know the opposite side (\(PQ = 77\)) and the adjacent side (\(OP=67\)) with respect to the angle \(x\). The tangent ratio is defined as \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan x=\frac{77}{67}\).

Step2: Solve for \(x\)

Take the inverse tangent (arctan) of both sides. \(x = \arctan(\frac{77}{67})\). Using a calculator, \(\frac{77}{67}\approx1.149\), and \(\arctan(1.149)\approx48.9^{\circ}\).

Answer:

\(48.9^{\circ}\)