Question

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 1

Since the angles add to 180°, angle F is 72°.

Using the law of sines,

DF/sin72° = 24/sin45°
x = 32.28

So, did you just guess at A?

This is just an answer from another website, but it should still work.

Answer 2

Answer:

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