Question

In triangle DEF, 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.

Answer 1

In order to use the Law of Sines, EF has to be the included side. Therefore, we need to calculate angle F which is 72 degrees.

side f / sine (F) = side d / sine (D)
side f / sine (72) = side 24 / sine (45)
side f = sine (72) * 24 / sine (45)
side f = 0.95106 * 24 / .70711
side f (DE) = 32.2798998741

answer is C