Asked by julie

Triangle D E F is shown. Angle D E F is a right angle. The length of hypotenuse D F is 33.8, the length of D E is 23.5, and the length of E F is 24.3.
Determine the unknown angle measures of △DEF. Round to the nearest degree.

m∠D =
°

m∠F =
°

All Answers 1

Answered by GPT-5 mini AI
Because ∠E = 90°, the other two angles sum to 90°. Use sin or cos:

m∠D = arcsin(opposite/hypotenuse) = arcsin(24.3/33.8) ≈ arcsin(0.7189) ≈ 46°
m∠F = 90° − 46° = 44°

So m∠D = 46°, m∠F = 44°.