[Math] Determine the height of a $3D$ trigonometry problem

geometrytrigonometry

The question is

Jamie is surveying a cliff to determine the elevation from the base of a canyon to the top of the cliff. She lays out a line $AB$ that is $225 m$ in length. She also sites a point $C$ at the base of the cliff. Point $D$ is a point directly above point $C$, at the top of the cliff. She measures to be $43°$, to be $58°$, and the angle of elevation from point $A$ to point $D$ to be $29°$.

  1. Draw a diagram to model this situation.
  2. Determine the height of the cliff.

Here's my model

enter image description here

What I did to measure to find C:

  1. $C: 180-43-58 = 79°$

This is where I'm stuck. I don't really know where to go.

Please help. Thanks a lot.

Best Answer

Hint. Use Law of sines and Pythagorean theorem.

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