Question

A boy is standing on the ground and flying a kite with $100m$ of string at an elevation of ${30}^{\circ }$. Another boy is standing on the roof of a $10m$ high building and is flying his kite at an elevation of ${45}^{\circ }$. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.

Answer 1

Let $L$ be the string of the kite

In $\Delta ABC$

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

$\therefore$ The height of the first kite above ground $=100m\times \sin {30}^{\circ }$

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

$=50m$

In $\Delta AFE$

$\Rightarrow \sin {45}^{\circ }=\frac{AF}{AE}$

$\therefore$ Height of 2nd kite $=L\sin {45}^{\circ }+10m$

$\Rightarrow L\sin {45}^{\circ }+10=50$

$\Rightarrow L\times \frac{1}{\sqrt{2}}=40$

$\therefore L=40\sqrt{2}m$