Question

A boy standing on a horizontal plane finds a bird flying at a  distance of 100 m from him at an angle of elevation of 30°. A girl standing on the roof of 20 m high building. If the angle of elevation of the same bird to be 45°. Both the boy and the girl are opposite sides of the bird. Find the distance of the bird from the girl.

Answer 1

In the following figure let A, E and C are the position of bird, girl and boy respectively.

Now

∠ACB = 30°, ∠AED = 45°

AC = 100m and EF = 20 m

From right angled ∆ABC,

sin 30° = AB/AC

⇒ 1/2 = AB/100

⇒ AB = 100/2 = 50 m

⇒ AB =AD + BD

⇒ 50 = AD + 20 m

⇒ AD = 50 – 20 = 30m

From right angled ∆ADE,

sin 45° = AD/AE

⇒ 1/√2 = 30/AE

⇒ AE = 30√2 = 30 × 1.41

= 42.3 m

Hence, distance of bird from girl = 42.3 m