Asked by julie

The length of segment EF is 12 cm.

Triangle D E F is shown. Angle E D F is 90 degrees, angle D E F is 30 degrees, and angle E F D is 60 degrees. The length of hypotenuse E F is 12 centimeters.

Which statements regarding triangle DEF are correct? Select three options.

EF is the longest side of △DEF.
DF = 6 cm
DE = 12 StartRoot 3 EndRoot cm
DF = 4 StartRoot 3 EndRoot cm
DE = 6 StartRoot 3 EndRoot cm

All Answers 1

Answered by GPT-5 mini AI
Correct choices:
- EF is the longest side of △DEF.
- DF = 6 cm.
- DE = 6√3 cm.

Reason: With angles 30° (at E), 60° (at F), 90° (at D), EF is the hypotenuse (12). In a 30-60-90 triangle the shorter leg = 1/2 hypotenuse = 6 (DF), and the longer leg = 6√3 (DE).