Question

From a point A on the ground, the angles of elevation of the top of a $10m$ tall building and helicopter hovering at some height of the building are ${30}^{\circ }$ and ${60}^{\circ }$ respectively. Find the height of the helicopter above the building.

• A. $10\sqrt{3}$
• B. $20(3+\sqrt{3})m$
• C. $20m$
• D. $30m$

Answer 1

The correct option is C $20m$

Let the height of helicopter be $h$
height of building $=10m$
Angle of elevation of the building = ${30}^{\circ }$
Angle of elevation of the helicopter = ${60}^{\circ }$
Let distance between the point and the building = $d$
Now, $\tan \angle$ of elevation = $\frac{height}{distance}$
Thus, $\tan 30=\frac{10}{d}$
$d=10\sqrt{3}$
$\tan 60=\frac{h+10}{d}$
$\sqrt{3}=\frac{h+10}{10\sqrt{3}}$
$h=20$ m