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Two lamp-posts are of equal height. A boy measured the elevation of the top of each lamp-post from the mid-point of the line-segment joining the feet of lamp-post as $30 °$ . After walking $15 m$ towards one of them, he measured the elevation of the top of nearest lamp-post at the point where he stands as $60 °$ . Determine the height of each lamp-post and the distance between them.

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1732 m

1632 m

1532 m

1832 m

answer is A.

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Detailed Solution

Given that two lamp-posts are of equal height. A boy measured the elevation of the top of each lamp-post from the mid-point of the line-segment joining the feet of lamp-post as

30 °

After walking 15m towards one of them, he measured the elevation of the top of nearest lamp-post at the point where he stands as

60 ° .

We have to find the height of each lamp-post and the distance between them.
Question Image

In a right-angle triangle,

tan θ = Opposite side Adjacent side .

Let the height of the lamp be h m and the distance between the posts be 2d m.

tan 30 o = h d ⇒ 13 = h d ⇒ d = h 3 tan 60 o = h d − 15 ⇒ 3 = h d − 15 ⇒ d 3 − 153 = h ⇒ 3 h − 153 = h ⇒ 2 h = 153 ∴ h = 1532

d = h 3 ∴ d = 452 H e n c e, 2 d = 45

The height of the light house is

1532 m

and the distance between the lamp posts is 45 m.
Therefore, the correct option is 1.

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