Question

35) A person X standing on the ground observes a bird flying at a distance of 200m
from him at an angle of elevation of 30°. At the same moment, another person
Y
standing on the roof of a building of height 50m, finds the angle of elevation of the
same bird to be 45°. If both are standing opposite to each other on either side of the
bird, find the distance of the bird from Y. Also find the distance at which X is
standing from the building.
F THE
200m
L45 SY
P
30°
50m
M M
X
Q​

Answer 1

R.E.F image

For ΔXBA,

sin30

∘

=

XB

BA

as sinθ=

hyp

OPP

2

1

=

100

BA

2

100

=BA

50m=BA

For ΔBYD,

sin45

∘

=

BY

BD

2

1

=

BY

BA−AD

2

1

=

BY

BA−YC

[as AD=YC]

2

1

=

a

50−20

a=30 √2

m

∴ The distance of the bird from

Y is 30 √2 m