Q9 of 61 Page 215

A person X standing on a horizontal plane, observes a bird flying at a distance of 100 m from him at an angle of elevation of 30c. Another person Y standing on the roof of a 20 m high building, observes the bird at the same time at an angle of elevation of 45°. If X and Y are on the opposite sides of the bird, then find the distance of the bird from Y.


Given, AC = 700 m and EF = ?


Let position of person X be B, position of person Y be F and AE = x.


In triangle ABC


∠ABC = 30°


We know,





⇒ 100 = 2 (x + 20)


⇒ 100 = 2x + 40


⇒ 2x = 60


⇒ x = 30


And, in triangle AFE,


∠AFE = 45°





⇒ EF = 30√2


∴ Distance of the bird from Y is 30√2 m.


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