Question

find ( mangle r ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle r=square^{circ} )

Explanation:

Step1: Use the tangent function

In a right - triangle \(PQR\) with \(\angle Q = 90^{\circ}\), \(\tan R=\frac{opposite}{adjacent}\). The side opposite to \(\angle R\) is \(PQ = 4\) and the side adjacent to \(\angle R\) is \(QR=5\). So, \(\tan R=\frac{PQ}{QR}\).

Step2: Calculate the angle

We know that \(R=\arctan(\frac{PQ}{QR})\). Substituting \(PQ = 4\) and \(QR = 5\), we get \(R=\arctan(\frac{4}{5})\). Using a calculator, \(\arctan(0.8)\approx38.7^{\circ}\)

Answer:

\(38.7\)