In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=17°, and RS = 84 feet. Find the length of QR to the nearest tenth of a foot.

The length of QR to the nearest tenth of a foot is 287.28 feet.

Step-by-step explanation:

Let a right angled Triangle QRS have base SQ, perpendicular RS and Hypotenuse QR.

∠S = 90°

∠Q = 17°

Perpendicular = 84 ft

We know that for a right angle triangle

SinΘ = perpendicular/Hypotenuse

Sin ∠Q = 84/QR

QR = 84/sin (17°)

QR = 84/0.2924

QR = 287.2777

QR = 287.28 feet