Question

2.
A flag staff stands vertically on a pillar. The
height of the flag staff being double the height
of the pillar. A man on the ground at a distance
finds both pillar and the flag staff subtends
equal angle 'e'at his eye then 6 =​

Answer 1

Given :  A flag staff stands vertically on a pillar.

The height of the flag staff being double the height of the pillar.

A man on the ground at a distance d finds both pillar and the flag staff subtends equal angle 'e'at his eye

To Find :  e

Solution:

Let say height of pillar =   x

Height of flag staff = 2x

tan e  = x/d

tan ( e+ e )  = (x + 2x)/d

=> tan 2e  = 3x/d

=> tan2e/tane  = 3

=> tan2e  = 3tane

=> 2tane/(1 - tan²e)  = 3tane

=> 2 = 3(1 - tan²e)

=> 2 = 3 - 3tan²e

=> 3tan²e  = 1

=> tan²e = 1/3

=> tane  = 1/√3

=> e = 30°

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