Question

Amit, standing on a horizontal plane, find 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, find the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. find the distance of the bird from Deepak.​

Answer 1

Deepak is at a distance of 50√2m from the bird. So, 50√2 m is the answer.

Answer 2

Solution:-

Let Amit is standing at point A, bird at point B, deepak at point D

height of the bird = BC, let E be a point on BC corresponding to point D at 50 m height

given,

AB = 200

∠A = 30°

∠D = 45°

In triangle ABC

Sin 30 = BC/AB

=> 1/2 = BC/200

=> BC = 100 m

=> BE = BC- EC = 100 - 50 = 50 m

In triangle,BED,

sin 45 = BE/BD

=> 1/√2 = 50/BD

=> BD = 50√2 = 70.7 m

Hence the distance of the bird from deepak is 70.7 m or approx 71

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@GauravSaxena01