Question

The length of a string between a kite and a point on the roof of a building $10m$ high is $180m$. If the string makes an angle $\theta$ with the level ground such that $\tan \theta =\frac{4}{3}$, how high is the kite from the ground?

• A. $154m$
• B. $176m$
• C. $198m$
• D. $214m$

Answer 1

The correct option is A $154m$

$\tan \theta =\frac{4}{3}$
Hence
$\sin \theta =\frac{4}{5}$ and $\cos \theta =\frac{3}{5}$
Hence the perpendicular height of the kite from the rooftop of the building is
$=180\sin \theta$
$=180.\frac{4}{5}$
$=36\left(4\right)=144m$
Hence the height of the kite from the ground will be
$=$ Height of the building $+$ height of the kite from the rooftop of the building.
$=144+10$
$=154m$