In ΔBCD, the measure of ∠D=90°, the measure of ∠B=71°, and DB = 67 feet. Find the length of BC to the nearest tenth of a foot.

6 .8 ft

Step-by-step explanation:

We are given two of the angles of the triangle so since all angles of a triangle add up to 180, we can find the measure of ∠B:

∠B + ∠C + ∠D = 180

∠B + 42 + 90 = 180

∠B = 180 - 90 - 42 = 48°

We want to find DB, and we already know CD = 7.5, so let's use the Law of Sines, which states that for a triangle with sides a, b, and c and angles A, B, and C: . Let's use that concept here:

Cross-multiply and solve:

DB * sin(48) = 7.5 * sin(42)

DB ≈ 6.75 ≈ 6.8 ft