Question

The angle of elevation of point $A$ with the top of the hill is ${80}^o$. $B$ is the point at a distance of $200m$ vertically above $A$. If the angle of elevation of the point $B$ with the top of the hill is ${60}^o$. Find the height of the hill and the distance of point $A$ from the bottom of the hill.
$(\tan {80}^o=5.67,\tan {60}^o=1.73)$

Answer 1

Let $AO=BE=x$

$\therefore \tan {80}^o=\frac{h}{x}=2.75$

$\therefore h=2.75x$

$\therefore \tan {60}^o=\frac{h-200}{x};\left(1.73\right)x=h-200$

$\therefore 1.73x=2.75x-200$

$\therefore 200=1.02x$

$\therefore x=\frac{200}{1.02}=196.07m=$ distance between bottom

$\therefore h=\left(2.75\right)\left(196.07\right)=539.1925$

Height of hill $=539.1925m$