In ΔBCD, the measure of ∠D=90°, the measure of ∠B=75°, and CD = 97 feet. Find the length of BC to the nearest tenth of a foot.

100.42 feet

Step-by-step explanation:

Since the triangle has a right angle, we may find the length of the unknown side using the trigonometric notations SOH CAH TOA where

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

Given that the measure of ∠D=90°, the measure of ∠B=75°, and CD = 97 feet

CD is the opposite side facing ∠B, BC is the hypotenuse side hence

Sin 75 = 97/BC

BC = 97/Sin 75°

= 100.42 feet