Let AB be the tower in the figure and C and D be two points on the straight line BD, at distances 5m and 20m from the foot of the tower AB. Now, join B, C, and C, D. We get two right-angled triangles both right angled at B. We use the trigonometric ratio tan by using AB as height and BC as a base(for ∆ABC) and AB as height and BD as a base(for ∆ABD) to find the height of the tower AB. By the problem we have, ∠ACB + ∠ADB = 90°.

In ∆ABC, we have

or,

or,

Also, from ∆ABD,

or,

Putting the value of tan∠ABD in the equation we get

or,

or,

a positive value is taken since the height of the tower can’t be negative.

The height of the tower AB = 10m.