Question

The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 36° find the height of the pole

Answer 1

119.45 m

Explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

`\triangle ABC` represents the 1st angle of elevation of sun i.e. 58°

`\triangle ABD` represents the 2nd angle of elevation of sun i.e. 36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB =
`h` m

Let side BC =
`x` m

Now, let us apply tangent rules in
`\triangle ABC, \triangle ABD` one by one:

`tan\theta = (Perpendicular)/(Base)\\\Rightarrow tan58^\circ=(AB)/(BC)\\\Rightarrow tan58^\circ=(h)/(x)\\\Rightarrow x = 0.624h ..... (1)`

`tan36^\circ = (h)/(x+90)`

Putting value of
`x` using equation (1):

`tan36^\circ = (h)/(0.624h+90)\\\Rightarrow 0.726* 0.624h+0.726* 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}`

119.45 m is the height of pole.