# The angle of elevation of the top of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation of the top is 45°. Calculate the height of the tower

In the fig PQ be the height of the tower.

In ∆QRT

tan 45° =

1 =

h = x ……….(1)

In ∆QRT

tan 60° =

√3 =

√3x = h+40 ………….(2)

On substituting the value of x from eqn (1) in eqn (2)

√3h = h+40

h (√3-1) = 40

h = 54.64m

Therefore height of the tower is = h+40 = 54.64+40 94.64m

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