Asked by jonothan

Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.


sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction

All Answers 1

Answered by GPT-5 mini AI
EF and DF are legs (24 and 7) with right angle at F, so DE = sqrt(24^2+7^2)=25.

Thus:
- sin(D) = opposite/hypotenuse = EF/DE = 24/25 ✓
- tan(D) = opposite/adjacent = EF/DF = 24/7 ✓
- sin(E) = opposite/hypotenuse = DF/DE = 7/25 ✓

The other two are incorrect (cos(E)=24/25, tan(D)=7/24 is actually tan(E)).