Question

find pr.

right triangle pqr with right angle at r, angle at p is 22 degrees, hypotenuse pq is 8

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

submit

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( PRQ \), \( \angle R = 90^\circ \), hypotenuse \( PQ = 8 \), and we need to find \( PR \) (adjacent side to \( \angle P = 22^\circ \)). The cosine ratio is \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(22^\circ)=\frac{PR}{PQ} \).

Step2: Substitute values and solve for \( PR \)

We know \( PQ = 8 \) and \( \theta = 22^\circ \). Substitute into the formula: \( PR = PQ\times\cos(22^\circ) \). Calculate \( \cos(22^\circ)\approx0.9272 \), then \( PR = 8\times0.9272\approx7.4 \).

Answer:

\( 7.4 \)