What is the height of the eagle nest? (Attn: All Engineers)

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What is the height of the eagle nest? (Attn: All Engineers)

If anyone has access to a laser rangefinder, could you please calculate the height of the nest? We need it to determine equipment needs for a nest camera.

With a known angle between the two readings, the height could be calculated using trigonometry. There may be an instrument that will do this without hand-calculating the geometry to derive the height.

If not, using simple algebra (Pythagorean Theorem).  Since the square of the hypotenuse is equal to the sum of the squares of the two remaining sides, it would be necessary to measure the distance from observer to the to the bottom of the tree (A), and from the same point, the distance diagonally upward to the nest (C). To calculate the third leg of the triangle (X), the first measurement would need to be a level line at ground level (impossible), or a level line at a known height (h) above the bottom of the tree (to provide a right angle with the trunk). The observer's height would then be added to the calculated height above the sight point.

Check my math-- it's been (too) many years since high school algebra. I won't dare try the trig without a slide rule-- do they still make them? Sorry I do not have superscripts -- ( ^2) means "squared."

(A ^2) + (X ^2) = (C ^2)  then solve for (X), which is the distance to nest above the sight point, and add the distance from the ground to the sight point. Simple?

(C ^2) / (A ^2) = (X ^2)

Square root of (X ^2) = (X), the distance up from sight point on tree trunk to nest
Then add distance from ground (h) + X  = height of nest.

Easy!!! My guess is 45 feet. Hope it is a little less.