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Amit, standing on a horizontal plane, finds a bird flying at a distance of $200 m$ from him at an elevation of $30 °$ . Deepak standing on the roof of a $50 m$ high building, finds the angle of elevation of the same bird to be $45 °$ . Amit and Deepak are on opposite sides of the bird, then the distance of the bird from Deepak is:

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50.7 m

60.7 m

70.7 m

80.7 m

answer is C.

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Detailed Solution

Given,
Length of the horizontal plane =200m
Angle of elevation =

30 °

.
Height of the building = 50m
The angle of elevation of the same bird to be

45 °

.
Consider the diagram,
Question Image

We know,

sinθ = \frac{Perpendicular}{Hypotenuse}

Let d be the distance between bird and point O which is the difference of distance between bird and point P and O,
d=BP-OP
Therefore,

d = 200 sin 30 ° − 50 ∵ sin 30 ° = 200 d ⇒ d = 2002 − 50 ∵ sin 30 ° = 12 ⇒ d = 100 − 50 ⇒ d = 50 m

The distance of bird from Deepak,

sin 45 ° = 50 distance ⇒ distance = 50 sin 45 ° ⇒ distance = 502 ⇒ distance = 70.7 m

Thus, the distance between the bird and Deepak is 70.7 m.
Therefore, option 3 is correct.

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