A boy standing on a horizontal plane find a bird flying at a distance of 100m from him at an - Maths - Some Applications of Trigonometry

Question

A boy standing on a horizontal plane find a
bird flying at a distance of 100m from him at an elevation of
30 â—¦
A girl standing on the roof of 20m high
building,find the angle of elevation of same bird to be 45
â—¦ Both the boy and the girl are on on opposite sides of the
bird find the distance of bird from the girl

Ajanta Trivedi · Accepted Answer

let the boy be at point B and the bird be at point A.

therefore AB=100 m.

let the distance between girl and bird be AF.

let the height of the building be FD = 20 m.

in the right triangle ACB,

$\sin 30 = \frac{A C}{A B} \frac{1}{2} = \frac{A C}{100} \Rightarrow A C = \frac{100}{2} = 50 m .$

AE=AC-EC

AE=AC-FD=50-20=30 m

now in the right angled triangle AEF,

$\sin 45 = \frac{A E}{A F} \frac{1}{\sqrt{2}} = \frac{30}{A F} A F = 30 \sqrt{2} = 30 * 1.414 = 42.42 m .$