Question

In triangle DEF, M angle D equals 44°, M angle E equals 61°, and EF equal 20 Inches. What is DE to the nearest 10th of an inch

Answer 1

The answer is DE = 27.81 in. Explanation: find the missing angle first, and put it into the equation for the law of sin ( sin(A)/a = sin(B)/b). Solve for the missing length, and you have the missing side to the triangle.

Answer 2

Applying the Law of sines, the length of DE to the nearest tenth is: 27.8 inches.

What is the Law of Sines?

The Law of sines is given as: sin D/d = sin E/e = sin F/f.

Given:

m∠D = 44°

m∠E = 61°

m∠F = 180 - 61 - 44 = 75°

EF = d = 20 in.

DE = f = ?

Plug in the values into the formula for the Law of sines:

sin 44/20 = sin 75/DE

Cross multiply

DE = (sin 75 × 20)/sin 44

DE = 27.8 inches

Therefore, applying the Law of sines, the length of DE to the nearest tenth is: 27.8 inches.

Learn more about the law of sines on: