Question

The string of a kite is $100$ m long and it makes an angle of 60${}^o$ with the horizontal. If there is no slack in the string, the height of the kite above the ground is _____

• A. $100$$\sqrt{3}$ m
• B. $50$$\sqrt{3}$ m
• C. $50$$\sqrt{2}$ m
• D. $100$ m

Answer 1

The correct option is B $50$$\sqrt{3}$ m

Let $AB$ be the string of the kite $B$ and $AC$ be the horizontal line.
$\therefore$BC$\perp$ AC, AB $=$ 100 m, $\angle$ $=$ 60${}^o$

$\sin {60}^o=\frac{BC}{AB}\Rightarrow \frac{\sqrt{3}}{2}=\frac{h}{100}\Rightarrow h=50\sqrt{3}$ m

$\therefore$ height of the kite above ground is 50$\sqrt{3}$ m

So, option B is correct.