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A sailor is going away from a lighthouse at a speed of 7[√3 -1] m/s. H

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| A sailor is going away from a lighthouse at a speed of 7[√3 -1] m/s. He observes that it takes him 30 seconds to change the angle of elevation of the top of the lighthouse from 60˚ to 45˚. What is the height of the light house?

A. 210√3 m

B. 210 m

C. 630 m

D. 70√3 m

Right Answer is: A

SOLUTION

Let the height of light house be x m.

then in ΔABC, tanC =

CD = 30[7(√3 -1)] = 210√3 – 210

Now, in ΔABD, tanD =

Now, BD = BC + CD

Hence, the height of lighthouse is 210√3 m.

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