# From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20 m high building are 45° and 60° respectively. Find the height of the transmission tower.

Since the building is vertical.
∠QPO = 90°

In a right-angled triangle, we know,

In ∆OPQ,

tan 45° =

1 =

OP = 20 -------(1)

Now in ∆OPR

tan 60° =

=

=

20√3 = h+20

h = 20√3-20

h = 20(√3-1) m.

Therefore the height of transmission tower is 20(√3-1) m.

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