How to Measure the Height of A Mountain?

How would one measure the height of a mountain if one only had a quadrant (for measuring angle)?

A Quadrant

A quadrant is as illustrated above.
Its a quarter of a disc with a scale along the curved arc, a plumb bob suspended from a pivot point and sighting vanes on the top edge.

A quadrant in use illustrated

It may be used to measure the angle to an elevation or to a star:

Measuring angle to mountain top using quadrant

I looked for an answer but could not find it online so I pieced together the information and filled in the gaps and hope this is correct.

Observe the figure (figure 1.1) below. You want to measure the height of the mountain (CD). You only have primitive hand made tools like a quadrant.
Step 1: You measure the angle to the top using a quadrant at point A
Step 2: And then after taking a 1000 steps (or 1000ft)
Step 3: You take the measurement of the angle at point B.

How would you find the height (CD) knowing AB=1000ft and angle(A) and angle(B)?:

Problem Illustrated Fig 1.1

The distilled equation from above is:

And an example illustrating above: