In triangle ΔDEF, m∠D = 45°, m∠E = 63°, and EF = 24 in. What is DE to the nearest tenth of an inch?

(1 point)
Responses

30.2 in.
30.2 in.

15.1 in
15.1 in

32.3 in.
32.3 in.

10.5 in.

1 answer

To find DE, we can use the Law of Sines. The formula is:

DE / sin(D) = EF / sin(E)

DE / sin(45) = 24 / sin(63)

DE / (sqrt(2)/2) = 24 / (sqrt(3)/2)

DE = (24 * sqrt(2)) / (sqrt(3))

DE ≈ 10.5 in.