Question

The length of a string between a kite and a point on the ground is $90$ m. If the string makes an angle $\theta$ with the level ground such that $\tan \theta =\frac{15}{8}$. Find the height of the kite.

Answer 1

Let, point $A$ be kite and point $B$ be on the ground

Length of the string be $AB=90$ m

Given, string makes an angle $\theta$ with the level of ground.

$\therefore \angle ABC={\theta }^{\circ }$

Now, $\tan \theta =\frac{AC}{BC}=\frac{15}{8}$ ....(Given)

Let $AC=15x$ m and $BC=8x$ m

Now, By Pythagorus theorem,

$(AB{)}^2=(AC{)}^2+(BC{)}^2$

$\Rightarrow (90{)}^2=(15x{)}^2+(8x{)}^2$

$\Rightarrow 8100=225x^2+64x^2$

$\Rightarrow 8100=289x^2$

$\Rightarrow x^2=\frac{8100}{289}$

$\Rightarrow x=\frac{90}{17}$

Therefore, $AC=15x=15\times \frac{90}{17}=79.41$ m

Height of the kite $=79.41$ m.