Question

what is m∠q?
enter your answer in degrees using deg, rounded to one decimal place.

Explanation:

Step1: Identify triangle type and sides

Triangle \( PRQ \) is right - angled at \( R \). Hypotenuse \( PQ = 34 \), opposite side to \( \angle Q \) is \( PR \), adjacent side is \( RQ = 30 \). First, find \( PR \) using Pythagorean theorem: \( PR=\sqrt{PQ^{2}-RQ^{2}}=\sqrt{34^{2}-30^{2}}=\sqrt{(34 + 30)(34 - 30)}=\sqrt{64\times4}=\sqrt{256}=16 \).

Step2: Use sine to find \( \angle Q \)

\( \sin Q=\frac{PR}{PQ}=\frac{16}{34}=\frac{8}{17}\approx0.4706 \). Then \( \angle Q=\arcsin(0.4706)\approx28.1^{\circ} \).

Answer:

\( 28.1^{\circ} \)