A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 300. A girl standing on the roof of 20 meter high building finds the angle of elevation of the same bird to be 450. Both the boy and the girl are on opposite sides of the bird. Find the distance of the bird from the girl.                                                                                                               

(Ans: 42.42m)

Ans:    In right ΔACB

Sin 30 =  AC/AB

1/2 = AC/100

2 AC = 100

AC = 50m

⇒ AF = (50 - 20) = 30m

In right Δ AFE

Sin 45 =  AF/ AE

1/√2  = 30/AE

AE = 30 √2

= 30 x 1.414

= 42.42m