Question

find pr.

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( RQP \), we know angle \( R = 40^\circ \), adjacent side to angle \( R \) is \( RQ = 6 \), and \( PR \) is the hypotenuse. We use the cosine function, which is defined as \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(40^\circ)=\frac{RQ}{PR} \).

Step2: Solve for \( PR \)

Substitute \( RQ = 6 \) and \( \theta = 40^\circ \) into the formula: \( \cos(40^\circ)=\frac{6}{PR} \). Rearranging for \( PR \), we get \( PR=\frac{6}{\cos(40^\circ)} \).

Step3: Calculate the value

Using a calculator, \( \cos(40^\circ)\approx0.7660 \). Then \( PR=\frac{6}{0.7660}\approx7.8 \).

Answer:

\( 7.8 \)