If the angles of elevation of a tower from two points distant a and (a b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is

Question

If the angles of elevation of a tower from two points distant a and (a > b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is

Philoid · Accepted Answer

Given BC = a and BD = b
Let the height AB = h
In right ΔABD,

tan θ =

tan 30° =

……………1

In Δ ABC

tan 60° =

√3 a = h………………2

Multiplying 1 and 2

h² = b × √ 3 a

h = √ab