The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 80 m, find the height of the first tree.

Question

The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45&#xB0;. If the height of the second tree is 80 m, find the height of the first tree.

Philoid · Accepted Answer

In the fig let CE be the height of the first tree

and AB is the height of the second tree.

In ∆ADE

tan 45° =

1 =

h = 60m

Therefore height of the first tree is 80-60 = 20m