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

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 )