Question

The length of the string between kite and a point on the ground is $90\text{m}$. If the string makes an angle with the level ground and $\sin \alpha =\frac{3}{5}$. Find the height of the kite, if there is no slack in the string.

Answer 1

Given that,

$AC=90\text{m}\angle ACB=\alpha \&\sin \alpha =\frac{3}{5}$

$AC=$ Length of the string.

Let, $AB$ be the height of the kite $h$ m.

$\begin{array}{c}\text{In}\Delta ABC,\\ \sin \alpha =\frac{3}{5}\\ \sin \alpha =\frac{3}{5}=\frac{P}{H}=\frac{AB}{AC}\\ \frac{3}{5}=\frac{h}{90}\\ 5h=90\times 3\\ h=\frac{90\times 3}{5}=18\times 3=54\text{m}\\ h=54\text{m}\\ AB=54\text{m}\end{array}$

Hence,

The height of the kite is $54\text{m}$.