Question

b) find angle q to the nearest degree

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan Q=\frac{opposite}{adjacent}\). Here, the side opposite to angle \(Q\) is \(PR = 13\) and the side adjacent to angle \(Q\) is \(QR=15\). So, \(\tan Q=\frac{PR}{QR}=\frac{13}{15}\).

Step2: Find the angle using the inverse tangent function

\(Q=\tan^{- 1}(\frac{13}{15})\). Using a calculator, \(\tan^{-1}(\frac{13}{15})\approx41.07^{\circ}\).

Answer:

\(41^{\circ}\)