A radio antenna stands on top of a building 300 m tall. 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 antenna? -
Answer & explanation
Correct answer: option 3
height of building = BC m , height of antenna = AB m
In triangle BCD
tan 45° = \(\frac{BC}{CD}\)
1 = \(\frac{BC}{CD}\)
As , BC = 300 m . so , BD is also 300 m
in triangle ACD
tan 60° = \(\frac{AC}{CD}\)
\(\sqrt{3}\) = \(\frac{AC}{CD}\)
\(\sqrt{3}\) = AC , CD = 300
So , AC = 300\(\sqrt{3}\)
AB = AC - BC
= 300\(\sqrt{3}\) - 300 = 300(1.732 - 1) = 300 x 0.732 = 219.6 m