A man is standing on the deck of a ship which is 10m above water level He observes the angle of elev...........

Quantitative Aptitude ( CCS) Trignometry

A man is standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a light house as 60⁰ and the angle of depression of the base of lighthouse as 30⁰. Find the height of the light house.

30m

40m

45m

38m

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Explanation:

Let AB is the light house and the man is standing at C so, ∠BCD = 60⁰ and ∠ACD = 30⁰.
Let BD = h
Height & Distances
In ΔADC, tan 30⁰ = 10/CD
⇒ 1/√3 = 10/CD ⇒ CD = 10√3m
In ΔBDC, tan 60⁰ = h/CD
⇒√3 = h/10√3
⇒ h = 30m
So the height of the light house is AB = AD + BD = 10 + 30 = 40m