Question

Triangle E D F is shown. Angle E D F is 43 degrees and angle D F E is 82 degrees. The length of D F is 15.

What is the measure of angle E?
m∠E =

°

What is the length of EF rounded to the nearest hundredth?
EF ≈

Answer 1

Part 1

Angles in a triangle add to 180 degrees, so

`m\angle E=180^(\circ)-82^(\circ)-43^(\circ)=55^(\circ)`

Part 2

By the Law of Sines,

`(EF)/(\sin 43^(\circ))=(15)/(\sin 55^(\circ))\\\\EF=(15 \sin 43^(\circ))/(\sin 55^(\circ))\\\\EF \approx 12.49`

Answer 2

What is the measure of angle E?

m∠E =

✔ 55

°

What is the length of EF rounded to the nearest hundredth?

EF ≈

✔ 12.49

Explanation: