Question

In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=37°, and SQ = 56 feet. Find the length of QR to the nearest tenth of a foot

Answer 1

70.1 ft

Explanation:

The cosine relation gives the ratio of the adjacent side to the hypotenuse for an acute angle in a right triangle:

Cos = Adjacent/Hypotenuse

cos(37°) = SQ/QR

Rearranging gives ...

QR = SQ/cos(37°) = (56 ft)/0.798636 = 70.1 ft

The length of QR is about 70.1 ft.