In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=77°, and QR = 95 feet. Find the length of RS to the nearest tenth of a foot.

Question

he,lp ghceiguecoeccenioceoihcenioecoce

Answer 1

Hi, Emma!

Law of Sines is applied, since the length of a side of the triangle is known, at least two interior angles' respective measures are known, and the length of another side must be found. For this particular problem, the Law of Sines must be used to find the length of RS, which is opposite of Angle Q, measuring 77 degrees.

sin(77°)/x = sin(90°)/95

x(sin(90°)) = 95(sin(77°))

(x)(sin(90))/(sin(90)) = ((95)(sin(77))/(sin(90))

x ≈ 92.6

The length of RS is approximately equal to 92.6 feet.