Question

A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 30°.A girl standing on the roof of 20cm high building. Finds the bird at an angle of elevation of 45°. Both are on pp. sides of the bird. Find the distance of bord from the girl.

Answer 1

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Answer 2

Answer:

Distance between girl and bird is  30√2 m = 42.43 m.

Step-by-step explanation:

Given: Distance between Boy and Bird = 100 m

           Height of building = 20 m

          Angle of elevation boy = 30°

          Angle of elevation girl = 45°

To find: Distance between Girl and Bird

Figure is attached.

In Δ ABC

using trigonometric ratio, we get

$sin\,30^{\circ}=\frac{AC}{AB}$

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

$AC=\frac{100}{2}$

AC = 50 m

⇒ AC = FA + CF ( from figure )

   50 =  FA + 20    ( ∵ CF = ED = 20 m )

    FA = 50- 20

    FA = 30 m

Now in Δ AEF

using trigonometric ratio, we get

$sin\,45^{\circ}=\frac{FA}{AE}$

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

AE = 30√2 = 42.43 m

Therefore, Distance between girl and bird is  30√2 m = 42.43 m.