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Two ships are sailing in the sea on either side of a lighthouse; the angles of depression of two ships as observed from the top of the lighthouse are 600 and 450 respectively. If the distance between the ships is 200(1+√3/√3)meters, find the height of the lighthouse. (Ans:200m)
Ans: In right Δ ABC
Tan 60 = h/BC
√3 = h/BC
⇒ H = √3 BC
In right Δ ABD
Tan 45 = h/BD
h = BD
BC + BD = 200 (1+√3/√3)
h = √3 BC
= √3 (200/√3)
= 200m
∴ height of light house = 200m
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