In ΔPQR, the measure of ∠R=90°, the measure of ∠P=52°, and QR = 9.6 feet. Find the length of RP to the nearest tenth of a foot.

Given:

In ΔPQR, the measure of ∠R=90°, the measure of ∠P=52°, and QR = 9.6 feet.

We need to determine the length of RP.

Length of RP:

The image of the triangle PQR is attached below.

Using the figure, the length of RP can be determined using the trigonometric ratio,

Substituting , and

Thus, we get;

Substituting the values, we get;

Simplifying, we get;

Dividing, we get;

Thus, the length of RP is 7.5 feet.