Mathematics: In triangle def measurement angle d = 45 degrees meausrement angle e = 63 degrees and ef = 24 inches. what is de to the nearest tenth of a inch?

answer: is 100 times more.step-by-step explanation:...

In triangle def measurement angle d = 45 degrees

poopybutt541

15.01.2022

DE = 32.8 inches is the answer.

Step-by-step explanation:

It is given that In the given triangle DEF, angle D = 45°, ∠E = 63° and EF = 24 inches.

We have to calculate the length of DE.

From the sine rule of a triangle

$\frac{sin D}{EF}=\frac{sinF}{DE}$

As we know sum of all angles of a triangle is 180°

Therefore ∠D + ∠E + ∠F = 180°

45 + 63 + F = 180

F = 180-108 = 72°

Now from the sine rule written above

$\frac{sin45}{24}=\frac{sin72}{DE}$

$\frac{0.71}{24}=\frac{0.95}{DE}$

.029 = .95/DE

DE = 0.95/0.029 = 32.75 ≈ 32.80 inches

Answer will be DE = 32.80 inches

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