Question

A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively α and β. Prove that the height of the top from the ground is

$\frac{(b-a)\tan \alpha \tan \beta }{\tan \alpha -\tan \beta }$.

Answer 1

Let OP be the tree and A, B be the two points such OA = a and OB = b and angle of elevation to the tops are α and β respectively. Let OL = x and PL = h

We have to prove the following

The corresponding figure is as follows

In

…… (1)

Again in

…… (2)

Subtracting equation (1) from (2) we get

Hence height of the top from ground is .