Question

I have no idea how to solve this one problem:

Round to two decimal places.

Two observers 25 feet apart, sight to the top of the tree. If the angle of elevation to the top of the tree from the observer closest to the tree is 30 degrees and the angle of elevation from the furthest observer is 20 degrees, how tall is the tree?

I got 98.48 feet but it is wrong, what is the correct answer and how would I go about solving this? Thank you!

Answer 1

Suppose the nearer observer is at a distance x, and the tree has height h. Then, it is clear that

h/x = tan30°
h/(x+25) = tan20°

Now, eliminate x and we see that

h/tan30° = h/tan20° - 25
h(cot20°-cot30°) = 25
h = 25/(cot20°-cot30°)
h = 24.62 ft