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A boy standing on a horizontal plane finds a bird, flying at a

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A boy standing on a horizontal plane finds a bird, flying at a distance of 100 m from him at an elevation of $3 0^{o}$ . A girl standing on the roof of a 20 m high building finds the angle of elevation of the same bird to be $4 5^{o}$ . Both the boy and the girl are on the opposite side of the bird. Find the distance of the bird from the girl.

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A boy standing on a horizontal plane finds a bird, flying at a distance of 100 m from him at an elevation of

3 0^{o}

. A girl standing on the roof of a 20 m high building finds the angle of elevation of the same bird to be

4 5^{o}

. Both the boy and the girl are on the opposite side of the bird. Find the distance of the bird from the girl.

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Text solutionVerified

Let A be the position of the bird and E and C be the positions of the girl and the boy, respectively.

Then,

∠ A CB = 3 0^{o}, ∠ A E D = 4 5^{o}, A C = 100 m, EF = 20 m

In right

△ A CB

we have,

sin 3 0^{o} = \frac{A B}{A C}

\frac{1}{2} = \frac{A B}{100}

A B = 50 m

A D = A B - B D

A D = 50 - EF

A D = 50 - 20 = 30 m

In right

△ A D E

, we have,

sin 4 5^{o} = \frac{A D}{A E}

\frac{1}{2} = \frac{30}{A E}

A E = 302 = 42.3 m

Therefore, the distance of bird from the girl is 42.3 m.

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Question Text	A boy standing on a horizontal plane finds a bird, flying at a distance of 100 m from him at an elevation of $3 0^{o}$ . A girl standing on the roof of a 20 m high building finds the angle of elevation of the same bird to be $4 5^{o}$ . Both the boy and the girl are on the opposite side of the bird. Find the distance of the bird from the girl.
Answer Type	Text solution:1
Upvotes	150