The angle of elevation of a tower becomes 60° from 45° by moving 60 metres towards a Minar. Find the height of the Minar.

Question: The angle of elevation of a tower becomes 60° from 45° by moving 60 metres towards a Minar. Find the height of the Minar.

Solution:

let, height AB
In triangle ABD,
tan60 = AB/BD
⇒ √3 = AB/BD
⇒ BD = AB/√3

In triangle ABC,
tan45 = AB/BC
⇒ 1 = AB/BC
⇒ AB = BC
⇒ AB = BD + DC
⇒ AB = BD + 60
⇒ AB = (AB/√3) + 60
⇒ AB - (AB/√3) = 60
⇒ AB . (√3 - 1)/√3 = 60
⇒ AB = 60√3/(√3 - 1)
= 60√3 (√3 + 1)/(√3 - 1)(√3 + 1)
= 30 (3 + √3) m