Two ships are on the opposite of a light house such that all three of them are collinear. The angles of depression of the two ships from the top of the light house are 30° and 60°. If the ships are 230√3 m apart, then find the height of the light house (in m).
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 172.5
Let the height of the light tower = h meter
The distance between the ships = 230√3 m
In triangle AOC
tan 30º = h/OC
1/√3 = h/OC
OC = √3h.......(1
In triangle AOB
Now, tan 60º = h/OB
√3 = h/OB
OB = h/√3.........(2
Equation 1 + Equation 2
OC + OB = h(√3 + (1/√3)) = 4h/√3
230√3 = 4h/√3
4h = 690
h = 172.5 m