Question

The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree whenseen from the top of the second tree is ${45}^{\circ }$. If the height of the second tree is 80 m, find the height of the first tree.

Answer 1

Let the difference between two trees be DE = 60 m and angle of depression of the first tree from the top to the top of the second tree is $\angle ABC=45$ .

Let BE = H m, AC = h m, AD = 80m.

We have to find the height of the first tree

The corresponding figure is as follows

In triangle ABC,

$tanB=\frac{AC}{BC}$

$tan45=\frac{h}{60}$

$1=\frac{h}{60}$

$h=60$

$SinceH=80-h$

$H=80-60=20m$

Hence the height of first tree is 20 m