Question

find m∠p.
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠p = °

Explanation:

Step1: Identify triangle type and sides

This is a right triangle \( \triangle PQR \) with \( \angle Q = 90^\circ \), \( PQ = 9 \), \( PR = 10 \). We can use trigonometric ratios. Let's find \( \cos(\angle P) \) since \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). Here, adjacent to \( \angle P \) is \( PQ = 9 \), hypotenuse is \( PR = 10 \). So \( \cos(\angle P)=\frac{9}{10} = 0.9 \).

Step2: Calculate \( \angle P \)

To find \( \angle P \), we take the inverse cosine (arccos) of \( 0.9 \). So \( \angle P=\arccos(0.9) \). Using a calculator, \( \arccos(0.9)\approx25.8^\circ \) (rounded to the nearest tenth).

Answer:

\( 25.8 \)