Question

find pq.
3.1
write your answer as an integer or as a decimal rounded to the nearest tenth.
pq =
submit

Explanation:

Step1: Identify adjacent side, angle

In right $\triangle PRQ$, $\angle P=65^\circ$, adjacent side to $\angle P$ is $PR=3.1$, and $PQ$ is the hypotenuse.

Step2: Use cosine trigonometric ratio

The cosine of an angle in a right triangle is $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. Substitute values:
$\cos(65^\circ)=\frac{3.1}{PQ}$

Step3: Rearrange to solve for PQ

Rearrange the formula to isolate $PQ$:
$PQ=\frac{3.1}{\cos(65^\circ)}$
Calculate $\cos(65^\circ)\approx0.4226$, so:
$PQ\approx\frac{3.1}{0.4226}\approx7.3$

Answer:

$PQ = 7.3$