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.
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.