Question

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

Explanation:

Step1: Identify adjacent side, angle

Adjacent to $\angle Q$: $QR=7$, $\angle Q=41^\circ$, $PQ$ is hypotenuse.

Step2: Use cosine definition

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(41^\circ)=\frac{7}{PQ}$

Step3: Rearrange to solve for PQ

$PQ=\frac{7}{\cos(41^\circ)}$

Step4: Calculate value

$\cos(41^\circ)\approx0.7547$, so $PQ\approx\frac{7}{0.7547}\approx9.3$

Answer:

$9.3$