Question

find m∠q.
p
9.4
r 4.2 q
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠q = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle PRQ \) with \( \angle R = 90^{\circ} \), hypotenuse \( PQ=9.4 \) and adjacent side to \( \angle Q \) is \( RQ = 4.2 \). We can use the cosine function, where \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So for \( \angle Q \), \( \cos(\angle Q)=\frac{RQ}{PQ}=\frac{4.2}{9.4} \)

Step2: Calculate the angle

First, calculate \( \frac{4.2}{9.4}\approx0.4468 \). Then, to find \( \angle Q \), we take the inverse cosine (arccos) of \( 0.4468 \). Using a calculator, \( \angle Q=\arccos(0.4468)\approx63.4^{\circ} \) (rounded to the nearest tenth)

Answer:

\( 63.4 \)