Question

The length of a string between a kite and a point on the ground is $90$ meters. If the string makes an angles $\theta$ with the ground level such that $\tan \theta =\frac{15}{8}$, how high is the kite? Assume that there is no slack in the string.

Answer 1

Let the length of the String be $AD$

and $AB$ be the Height

In $△ABD$

$\tan \theta =\frac{AB}{BD}\Rightarrow \frac{15}{8}=\frac{AB}{BD}$

$\Rightarrow AB=\frac{15}{8}BD..................\left(1\right)$

Also applying Pythagoras Theorem

$A{B}^2+B{D}^2=A{D}^2$

$\Rightarrow \frac{225}{64}B{D}^2+B{D}^2={90}^2$

$\Rightarrow \frac{289}{64}B{D}^2=8100$

$\Rightarrow \frac{17}{8}BD=90\Rightarrow BD=42.35$

Now, from $\left(1\right)$

$AB=\frac{15}{8}\times 42.35=79.40$