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A boy standing on the road observes a bird flying in east at an angle of 30°. After some time, he observes the same bird in the west at an angle of 60°. If the bird is flying at a constant height and distance covered by bird is 400 m, find the height at which bird is flying.

A boy standing on the road observes a bird flying in east at an angle of 30°. After some time, he observes the same bird in the west at an angle of 60°. If the bird is flying at a constant height and distance covered by bird is 400 m, find the height at which bird is flying. Correct Answer 100√3 m

Let height at which bird is flying is √3x,

tan30° = √3x/CB        

⇒ CB = √3x × 1/tan 30° = √3x × √3 = 3x

Also, tan60° = √3x/AC            

⇒ AC = √3x × 1/tan60° = √3x × 1/√3 = x

∴ AC + CB = x + 3x = 4x = 400 m

⇒ x = 100 m

∴ Height at which bird is flying = √3x = √3 × 100 m = 100√3 m. 

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