Question

In ΔBCD, the measure of ∠D=90°, the measure of ∠C=42°, and CD = 7.5 feet. Find the length of DB to the nearest tenth of a foot.

Answer 1

6.8 feet

Explanation:

Angle B: 180 - 90 - 42 = 48°

Using sine law:

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

DB = sin(42) × 7.5/sin(48)

DB = 6.753030332

Answer 2

6.8 ft

Explanation:

Draw a diagram first. See attachment.

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:
`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`. Let's use that concept here:

`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`

`(7.5)/(sin48) =(DB)/(sin42)`

Cross-multiply and solve:

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

DB ≈ 6.75 ≈ 6.8 ft