Question

a boy observes that the Angle of elevation of a bird flying at a distance of 100 m is 30° .at some distance from the boy ,a girl finds the angle of elevation of the same bird from a building 20 m high is 45° . find the distance of the bird from the girl .

Answer 1

At the same distance from the boy a girl finds the angle of elevation of the same bird from a building 20m high is 45degree.find the distance of the bird from the girl.

Answer 2

Answer: The distance of the bird from the girl is 86.60 m.

Step-by-step explanation:

since we have given that

Distance between the bird flying and the boy = 100 m

Angle of elevation that a boy observes = 30°

Height of building = 20 m

Angle of elevation of the same bird from a building = 45°

So, the figure is shown below:

In ΔABC, AC = 100 m

So, when we use "Trigonometric Ratio":

$\cos 30^\circ=\frac{BC}{AC}\\\\\frac{\sqrt{3}}{2}=\frac{BC}{100}\\\\BC=50\sqrt{3}\ m$

Since both having the equal base i.e. BC = DE = 50√3 m

Now, In ΔAED,

$\tan 45^\circ=\frac{AD}{DE}\\\\1=\frac{AD}{DE}\\\\AD=DE=50\sqrt{3}=86.60\ m$

Hence, the distance of the bird from the girl is 86.60 m.