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 45° and 60° respectively. Find the height of the tower.

Let BC is Building and AB is transmission tower.
In ΔBCD,
BC/CD = tan 45° ⇒ 20/CD = CD = 1
In ΔACD,
AC/ CD = tan 60° ⇒ AB+BC/CD = √3 ⇒ (AB+20)/20 = √3
⇒ AB + 20 = 20√3 ⇒ AB = 20(√3- 1)
Hence, the height of the transmission towwer is 20(√3- 1)m.