Answer:
- GF ≈ 11.2
- HD ≈4.3
- ∠HDE ≈68.8°
Step-by-step explanation:
The relevant trig relations are ...
Tan = Opposite/Adjacent
Sin = Opposite/Hypotenuse
These tell us ...
tan(43°) = GH/DG
GH = DG·tan(43°) = (12 cm)·tan(43°) ≈ 11.2 cm
and ...
sin(HDE) = EH/ED = (11.2 cm)/(12 cm)
∠HDE = arcsin(11.2/12) ≈ 68.8°
The length HD can be found from ...
tan(68.8°) = HE/HD
HD = HE/tan(68.8°) = (11.2 cm)/tan(68.8°) ≈ 4.3 cm
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Additional comments
The values shown in the solution here are rounded according to the problem statement. The values actually used in the calculations are the full-precision calculator values. Rounding is only done on the final answers.
