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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 $30^{\circ}.$ A girl standing on the roof of a $20\; m$ high building, finds the elevation of the same bird to be $45^{\circ}$ . The boy and the girl are on the opposite sides of the bird. Find the distance of the bird from the girl. (Given $\sqrt{2}=1.414$ )

Answers (1)

Let's assume the boy is standing on the ground at $A$ position of Bind is $B$

position of girl is $C.$

To find - Length $BC$

Given - $AB=100\; m$

$FC=DE=20\; m$

Solution - In $\Delta ABE$

$\sin 30^{\circ}=\frac{BE}{AB}\Rightarrow \frac{1}{2}=\frac{BE}{100}$

$BE=50\; m$

Now $BE=BD+DE$

$50=BD+20\; \; \; (DE=20\; m)$

$\Rightarrow BD=30\; m$

Now in $\Delta BDC$

$\sin 45^{\circ}=\frac{BD}{BC}\Rightarrow \frac{1}{\sqrt{2}}=\frac{30}{BC}$

$\Rightarrow BC=30\sqrt{2}\; m$

$\Rightarrow BC=30\times 1.414\; m$

$BC=42.42\; m$

Posted by

Safeer PP

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