Question

Calculate the height of a tree whose shadow is 20m shorter when the angle of elevation of the sun is 60° than when it's 30°.​

Answer 1

17.3 m

Explanation:

If t is the height of the tree, then the length of the shadow is ...

shadow length = t/tan(α)

where α is the angle of elevation. The difference in shadow lengths is ...

20 m = t/tan(30°) -t/tan(60°) = t(√3 -1/√3)

t = (20 m)/(2/√3) = 10√3 m ≈ 17.3 m

The tree is about 17.3 meters high.