The angle of elevation to the top of a tower 24√3 m high from two points on the level ground on its opposite sides are 45° and 60°. What is the distance (in m) between the two points?
Answer & explanation
Correct answer: option 3
⇒ AB = 24 \(\sqrt {3}\)
⇒ In Δ ABC:
tan 60° = \(\sqrt {3}\) : 1
(AB) (BC)
⇓ ⇓
24 \(\sqrt {3}\) (given) 24
⇒ In Δ ABD:
tan 45° = 1 : 1
(AB) (BD)
⇓ ⇓
24 \(\sqrt {3}\) (given) 24 \(\sqrt {3}\)
CD = BC + BD = 24 + 24\(\sqrt {3}\) = 24 (1 + \(\sqrt {3}\)) = 24 (1 + 1.732) = 24 (2.732) = 65.56