Question
A Navy captain going away from a lighthouse at the speed
of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60o to 45o. What is the height (in metres) of the lighthouse?Solution
Let height is H tan 600 = H / BD = BD = H / tan600 [BD = H / √3 tan 450 = AB / BC = AB = BC, BC = H 4(√3 – 1) m/s speed Time = 1 minute 60 Second Distance = Speed × Time = 4√3 – 1) × 60 = 240√3 – 240 CD = 240√3 – 60 CD = H – H/√3 = 240√3 – 240 H(√3 – 1) = 240√3(√3 – 1) H = 240√3 m
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