find ( mangle r ). \nwrite your answer as an integer or as a decimal rounded to the nearest tenth. \n(…

find ( mangle r ). \nwrite your answer as an integer or as a decimal rounded to the nearest tenth. \n( mangle r = square^circ )

find ( mangle r ). \nwrite your answer as an integer or as a decimal rounded to the nearest tenth. \n( mangle r = square^circ )

Answer

Explanation:

Step1: Identify the sides relative to ∠R

In right triangle ( \triangle PQR ) (right - angled at ( P )), for ( \angle R ), the adjacent side ( PR = 6 ) and the hypotenuse ( QR=9 ). We can use the cosine function, where ( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} ). So ( \cos(\angle R)=\frac{PR}{QR}=\frac{6}{9}=\frac{2}{3} ).

Step2: Find the measure of ∠R

To find ( \angle R ), we take the inverse cosine (arccos) of ( \frac{2}{3} ). Using a calculator, ( \angle R=\arccos\left(\frac{2}{3}\right) ). Calculating this, ( \arccos\left(\frac{2}{3}\right)\approx48.2^{\circ} ) (rounded to the nearest tenth).

Answer:

( 48.2 )