From a point 15 m above the water level, the angle of elevation of the top of a hill is 600 and the angle of depression of the base of the hill is 300 . What is the height of the hill?
Answer & explanation
Correct answer: option 4
AB represents height of hill and P is the point 15 m above water level
AB = AC + BC
∠CPB = ∠PCQ (PC is parallel to BQ)
PQ = BC
tan 30° = 1 : \(\sqrt {3}\)
(PQ) : (QC)
↓ ↓
15 ↓
15 × \(\sqrt {3}\) = 15 \(\sqrt {3}\)
QC = PB = 15 \(\sqrt {3}\) m
In Δ ABP; tan 60° = \(\sqrt {3}\) : 1 (PC = BQ)
(AB) : (PB)
↓ ↓
↓ 15 × \(\sqrt {3}\)
15 \(\sqrt {3}\) × \(\sqrt {3}\) = 15 × 3 = 45 m
Therefore, height of hill = 45 + 15 = 60 m