Question

A pole of 50 mtr high stands on the building 250 mtr high. to an observer at a height of 300 mtr the building and the pole subtend equal angles. then find the distance of the observer from top of the pole

Answer 1

Given:

A pole of 50 mtr high stands on the building 250 mtr high. to an observer at a height of 300 mtr the building and the pole subtend equal angles.

To find:

Find the distance of the observer from top of the pole

Solution:

Consider the attached figure while going through the following steps.

Let the distance be "x"

so, we have,

tan ∅ = 50/x

and

tan 2∅ = (250 + 50)/x

2tan ∅/(1 - tan ²∅) = 300/x

[2(50/x)] / [1 - (50/x)²] = 300/x

100/x = 300/x (1 - 2500/x²)

1 - 2500/x² = 1/3

2500/x² = 2/3

x² = 3750

x = 25√6

Therefore, the distance of the observer from top of the pole is 25√6 m