Anil looked up at the top of a lighthouse from his boat and found the angle of elevation to be 30 degrees. After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45 degrees. Find the height of the lighthouse.
  • a)
    25
  • b)
    25√3
  • c)
    25(√3-1)
  • d)
    25(√3+1)
Correct answer is option 'D'. Can you explain this answer?

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Answers

Kunaal Satija
Sep 15, 2021
If we look at the above image, A is the previous position of the boat. Angle of elevation from this point to the top of the light house is 30 degrees.
After sailing for 50 m, Anil reaches point D from where angle of elevation is 45 degrees. C is the top of the light house.
Let BD = x
Now, we know tan 30 degrees = 1/ √3 = BC/AB
Tan 45 degrees = 1
=> BC = BD = x
Thus, 1/ √3 = BC/AB = BC / (AD+DB) = x / (50 + x)
Thus x (√3 -1) = 50 or x= 25(√3 +1) m
The answer is Option D.

If we look at the above image, A is the previous position of the boat. Angle of elevation from this point to the top of the light house is 30 degrees.After sailing for 50 m, Anil reaches point D from where angle of elevation is 45 degrees. C is the top of the light house.Let BD = xNow, we know tan 30 degrees = 1/ √3 = BC/ABTan 45 degrees = 1=> BC = BD = xThus, 1/ √3 = BC/AB = BC / (AD+DB) = x / (50 + x)Thus x (√3 -1) = 50 or x= 25(√3 +1) mThe answer is Option D.
If we look at the above image, A is the previous position of the boat. Angle of elevation from this point to the top of the light house is 30 degrees.After sailing for 50 m, Anil reaches point D from where angle of elevation is 45 degrees. C is the top of the light house.Let BD = xNow, we know tan 30 degrees = 1/ √3 = BC/ABTan 45 degrees = 1=> BC = BD = xThus, 1/ √3 = BC/AB = BC / (AD+DB) = x / (50 + x)Thus x (√3 -1) = 50 or x= 25(√3 +1) mThe answer is Option D.