Answer:
- EF = 4.1
- DE = 9.1
- m∠F = 66°
Explanation:
The hypotenuse and one acute angle are given. The relevant relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
__
For the given triangle, these tell us ...
sin(24°) = EF/DF = EF/10
EF = 10·sin(24°) ≈ 4.1
and ...
cos(24°) = DE/DF = DE/10
DE = 10·cos(24°) ≈ 9.1
The remaining acute angle is the complement of the given one:
F = 90° -D = 90° -24°
∠F = 66°