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?
Answer & explanation
Correct answer: option 2
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