Answer:
6.8 ft
Step-by-step 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: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]. Let's use that concept here:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
[tex]\frac{7.5}{sin48} =\frac{DB}{sin42}[/tex]
Cross-multiply and solve:
DB * sin(48) = 7.5 * sin(42)
DB ≈ 6.75 ≈ 6.8 ft
