Question

The string of a kite $100$ metres long and it makes an angle of ${60}^{\circ }$ with the horizontal. Find the height of the kite.

• A. $86.5\text{m}$
• B. $90.5\text{m}$
• C. $80\text{m}$
• D. $75\text{m}$

Answer 1

Answer: (A)

$86.5\text{m}$

Given, $OK$ is $100\text{m}$ and the angle of elevation at O is ${60}^{\circ }$

Let the height of the kite be $h$

In right $\Delta OKP$

$\sin {60}^{\circ }=\frac{h}{100}$

$⟹h=100\sin {60}^{\circ }$

$⟹h=100\times \frac{\sqrt{3}}{2}$

$⟹h=100\times \frac{1.732}{2}$

$⟹h=86.5\text{m}$