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.

2 answers

To find DE, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Let x be the length of side DE. Then, we can set up the following proportion:

sin 63° / 24 = sin 45° / x

Simplifying, we get:

x = 24 sin 45° / sin 63°

Using a calculator, we get:

x ≈ 15.1

Therefore, the answer is B. 15.1 in (rounded to the nearest tenth).
AAAaannndd the bot gets it wrong yet again!

Total misuse of the law of sines.
∡E = 72°
so
DE/sin72° = 24/sin45°