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.

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,

$\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49$