The length of shadow of a tower standing on the ground is found to be 60 metres more when the sun's angle of elevation changes from `30^(@)` to `45^(@)`. Find the height of the tower.

Explanation

Let AB be the tower and BD and BC are the shadow of AB when the sun's angles of elevation are `30^(@) and 45^(@)` respectively.
Now, from the right-angled triangle ABC we get,
`tan 45^(@) = (AB)/(BC)` [ by definition ]
or, `1 = (AB)/(BC) `
or, BC = AB ............(1)
Again, from the right-angled triangle ABD, we get,
`tan 30^(@) = (AB)/(BD)` [ by definition ]
or, `(1)/(sqrt(3)) = (AB)/(BD) " " or, sqrt(3)AB = BD` or, `sqrt(3)AB = BC + CD`
or, `sqrt(3)AB = AB + 60 " " or, sqrt(3)AB - AB = 60 " " or, AB(sqrt(3)-1) = 60`
or, `AB = (60)/(sqrt(3)-1) xx (sqrt(3) + 1)/(sqrt(3) + 1)`
or, `AB = (60(sqrt(3)+1))/(3-1)= (60(sqrt(3)+1))/(2) = 30(sqrt(3) + 1)`
= 30(1.732 + 1) = `30 xx 2.732`
= 81.96
Hence the height of tower is 81.96 metres (approx.).