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.
AAAaannndd the bot gets it wrong yet again!
Total misuse of the law of sines.
∡E = 72°
so
DE/sin72° = 24/sin45°
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).