A tower T 1 of height 60 m is located exactly opposite to a tower T 2 of height 80 m on a straight road. From the top of T 1 , if the angle of depression of the foot of T 2 is twice the angle of elevation of the top of T 2 , then the width (in m ) of the road between the feet of the towers T 1 and T 2 is

Step-by-step solution

Let, the width of the road the road is d . If the angle of the elevation is θ , then tan θ = 20 d , here 20 is the difference between the heights of T 1 and T 2 . Given that, the angle of depression is twice of the angle of elevation. tan ⁡ 2 θ = 60 d We know, tan ⁡ 2 θ = 2 tan ⁡ θ 1 - tan 2 ⁡ θ ∴ 60 d = 40 / d 1 - 400 / d 2 ⇒ 400 d 2 = 1 3 d = 20 3