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A boy standing on a horizontal plane finds a bird flying at a distance of $100 m$ from him at an elevation of $30 °$ . A girl standing on the roof of a $20 m$ high building, finds the elevation of the same bird to be $45 ° .$ The boy and the girl are on the opposite sides of the bird, then distance of the bird from the girl is:

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22.42 m

52.42 m

32.42 m

42.42 m

answer is C.

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Detailed Solution

Given,
Distance of a horizontal plane =

100 m

Angle of elevation of

30 °

Height of building =

20 m

Angle of elevation of the same bird =

45 ° .

Consider the figure,
Question Image

We know,

sinθ = \frac{Perpendicular}{Hypotenuse}

Let ‘d’ be the distance between bird and point D which would be the difference of distance between bird and boy and 20m,
d=AB-DB
Therefore,

d = 100 sin 30 ° − 20 ∵ sin 30 ° = d 100 ⇒ d = 1002 − 20 ∵ sin 30 ° = 12 ⇒ d = 50 − 20 ⇒ d = 30 m

The distance of bird from girl,

sin 45 ° = 30 distance ⇒ distance = 30 sin 45 ° ⇒ distance = 302 ⇒ distance = 42.42 m

Thus, the distance of bird from girl is 42.42 m.
Therefore, option 3 is correct.

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