Question

A boy is standing on a horizontal plane and finds a bird flying at a distance of 100m from him at an elevation of 30 degree . a girl standing on a roof of 20m tall building finds the elevation of the same bird to be 45 degree. both thew boy and the girl are on opposite sides of the bird . find the distance of bird from the girl.

Answer 1

Answer:

42.426 m

Step-by-step explanation:

Let E be the position of the bird

A be the position of the boy

D  be the position of the girl

DC be the building at which the girl is standing.  

A boy is standing on a horizontal plane and finds a bird flying at a distance of 100 m from him i.e. AE = 100 m

DC = 20 =FB

In ΔABE

$sin \theta = \frac{Perpendicular}{Hypotenuse}$

$sin 30^{\circ} = \frac{EB}{AE}$

$\frac{1}{2} = \frac{EB}{100}$

$50= EB/tex]</p><p>EB = EF+FB </p><p>50=EF+20</p><p>EF =30 m</p><p><strong>In ΔFED</strong></p><p>[tex]sin \theta = \frac{Perpendicular}{Hypotenuse}$

$sin 45^{\circ} = \frac{EF}{ED}$

$\frac{1}{\sqrt{2}}= \frac{30}{ED}$

$ED= \frac{30}{\frac{1}{\sqrt{2}}}$

$ED= 42.426$

Hence the distance of bird from the girl is 42.426 m