Respuesta :

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

_____

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.

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