A boy standing on level ground finds a bird flying at a distance of 100m from him at an angle of elevation of 30.at the sa me time a girl standing on the roof of a 20m high building,finds the angle of elevation of the same bird to be 45.if the boy and the girl are on opposites sides of the bird,find the distance of the bird from the girl



The distance between the girl and the bird is 42.43m.

By pythagoras theorem height of the bird h is found by the formula,
thus h=50m.
Height of the bird from the top of the building then becomes 50-20=30m.
Again by Pythagoras theorem,
sin(45)=30/x, where x=distance of bird from the girl.
thus, x=42.43m.