A radio antenna of height 150 m stands on top of a building. At a point on the ground, the angle of elevation of bottom of antenna is 45° and the top of antenna is 60°. What is the height of the building?

75(√3 + 1) m

tan 45°  =        1      :       1

                     (BC)          (CD)  =  x

tan 60°  =        \(\sqrt {3}\)      :       1

                     (AC)          (CD)                         

                       ↓                ↓

                     \(\sqrt {3}\)x      = x

AB = AC - BC

150 = \(\sqrt {3}\)x - x

⇒ x = \(\frac{150}{\sqrt {3} - 1}\)

⇒ x = 75 (\(\sqrt {3}\) + 1) m