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

A. 30.2 in.
B. 15.1 in.
C. 32.3 in.
D. 10.5 in.

1 answer

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

a/sinA = b/sinB = c/sinC

In this case, we are given EF = 24 in and angles D and E, so we can find the length of DE.

Let x be the length of DE.

Therefore, we can set up the proportion:

24/sin(45°) = x/sin(63°)

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

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

x ≈ 15.1 inorB.

Therefore, the length of DE to the nearest tenth of an inch is 15.1 in.