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

Explanation

Let {DC} be the tower and {BC} be the building. Then, `angle {CAB}=45^{circ}`, `angle {DAB}=60^{circ}`, {BC}=20 {m}

Let height of the tower, {DC}={hm}.

In right triangle {ABC},

`tan 45^{circ}=frac{{BC}}{{AB}}`

`1=frac{20}{A B}`

{AB}=20 {m}

In right triangle {ABD},

`tan 60^{circ}=frac{{BD}}{{AB}}`

...