Anil looked up at the top of a lighthouse from his boat, and found the angle of

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Anil looked up at the top of a lighthouse from his boat, and found the angle of elevation to be 30

^{\circ}

. After sailing in a straight line 50 m towards the lighthouse, he found that the angle of elevation changed to 45

^{\circ}

. Find the height of the lighthouse.

Options:

A . 25

B . 25√3

C . 25(√3 - 1)

D . 25(√3 + 1)

Answer: Option D
:
D

Anil Looked Up At The Top Of A Lighthouse From His Boat, And...

Now since tan 45 = 1,BC=DB=x
Also, tan 30 =

\frac{1}{\sqrt{3}} = \frac{x}{50 + x}

Thus x(

\sqrt{3}

- 1) = 50
or, x = 25(

\sqrt{3}

+ 1)m

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