A boat is sailing towards a lighthouse of height 20√3 m at a certain speed. The angle of elevation of the top of the lighthouse changes fro… — Answer & Discussion

A boat is sailing towards a lighthouse of height 20√3 m at a certain speed. The angle of elevation of the top of the lighthouse changes from 30° to 60° in 10 seconds. What is the time taken (in seconds) by the boat to reach the lighthouse from its initial position?

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Discussion 1

CCommunity25 Jun 2019

Let the point where the angle of elevation of the boat is 60°be A

And the point where the angle of elevation of the boat is 30°be B

Also, let the top of lighthouse be O and bottom be C

Given: height of lighthouse = 20√3 m

In ?AOC

⇒ tan60° = 20√3/BC

⇒ √3 = 20√3/BC

⇒ BC = 20 m

In ?AOC

⇒ tan30° = 20√3/AC

⇒ 1/√3 = 20√3/AC

⇒ AC = 60 m

Now, time taken to cover AB = 10 sec

So, speed of boat = (60 - 20)/10 = 4m/s

∴ Time taken by the boat to go from A to C = 60/4 = 15 seconds