Question

Two poles of equal heights are standing opposite each other on either side of the road, which is 85 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles. (Use `sqrt(3)` = 1.73)

Answer 1

Let AB and CD be two poles of the same height ‘h’.

In ΔABE

tan 60° = `h/x`

`sqrt(3) = h/x`

h = `xsqrt(3)`   ...(1)

In ΔCED

tan 30° = `h/(85 - x)`

`1/sqrt(3) = h/(85 - x)`

`hsqrt(3) = 85 - x`   ...(2)

Substitute the value of h in equation (2) from equation (1)

`sqrt(3)x.sqrt(3) = 85 - x`

3x + x = 85

4x = 85

x = `85/4`

x = 21.25 m

From equation (1)

h = `xsqrt(3)`

h = 21.25 × 1.73

h = 36.7625

h = 36.76 m

x = 21.25 m

And other distances  = 85 – 21.25

= 63.75 m