Question

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

Explanation:

Step1: Identify the triangle type and trigonometric ratio

We have a right - triangle \( \triangle PRQ \) with \( \angle R = 90^{\circ} \), \( \angle P=34^{\circ} \), and hypotenuse \( PQ = 9 \). We want to find the length of \( PR \), which is the adjacent side to the angle \( \angle P \). The cosine of an angle in a right - triangle is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(34^{\circ})=\frac{PR}{PQ} \).

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

We know that \( PQ = 9 \) and \( \theta = 34^{\circ} \). Substituting these values into the cosine formula: \( PR=PQ\times\cos(34^{\circ}) \).
We know that \( \cos(34^{\circ})\approx0.8290 \) (using a calculator). Then \( PR = 9\times0.8290=7.461 \). Rounding to the nearest tenth, we get \( PR\approx7.5 \).

Answer:

\( 7.5 \)