To find DE, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
First, we can find the measure of angle F by subtracting the measures of angles D and E from 180°:
m∠F = 180° - 45° - 63° = 72°
Using the Law of Sines, we can set up the following proportion:
DE / sin(45°) = 24 / sin(72°)
We know that sin(45°) = sqrt(2) / 2 and sin(72°) is approximately 0.9511, so we can substitute these values into the proportion:
DE / (sqrt(2) / 2) = 24 / 0.9511
Simplifying this equation, we get:
DE = (24 * sqrt(2) / 2) / 0.9511
DE ≈ 15.1084
Rounding to the nearest tenth, DE ≈ 15.1 in
Therefore, the answer is 15.1 in.
In triangle ΔDEF, m∠D = 45°, m∠E = 63°, and EF = 24 in. What is DE to the nearest tenth of an inch?
30.2 in.
30.2 in.
15.1 in
15.1 in
32.3 in.
32.3 in.
10.5 in.
1 answer