Question

find ( mangle r ).

write your answer as an integer or as a decimal rounded to the nearest tenth.

( mangle r=) 。

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(RTS\) (\(\angle T = 90^{\circ}\)), we know the opposite side (\(TS = 7\)) and the adjacent side (\(RT=6\)) with respect to \(\angle R\). The tangent ratio is defined as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan R=\frac{TS}{RT}\).

Step2: Substitute the values

Substitute \(TS = 7\) and \(RT = 6\) into the tangent formula. We get \(\tan R=\frac{7}{6}\).

Step3: Find the angle using the inverse tangent function

If \(\tan R=\frac{7}{6}\), then \(R=\tan^{- 1}(\frac{7}{6})\). Using a calculator, \(\tan^{-1}(\frac{7}{6})\approx49.4^{\circ}\) (rounded to the nearest tenth).

Answer:

\(49.4\)