A boy standing on a horizontal plane find a bird flying at a distance of 100m from him at an elevation of 30 ◦ .A girl standing on the roof of 20m high building,find the angle of elevation of same bird to be 45 ◦ .Both the boy and the girl are on on opposite sides of the bird .find the distance of bird from the girl.

let the boy be at point B and the bird be at point A.

therefore AB=100 m.

let the distance between girl and bird be AF.

let the height of the building be FD = 20 m.

in the right triangle ACB,

AE=AC-EC

AE=AC-FD=50-20=30 m

now in the right angled triangle AEF,

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