Question

From a point P on the ground, the angles of elevation of the top of 20m tall building and of a helicopter, hovering at some height above the top of the building are ${30}^0$ and ${60}^0$ respectively. Find the height at which the helicopter is hovering. (above the ground)

Answer 1

Let the height of plane be $h$m

$\tan {30}^{\circ }=\frac{DB}{PB}\Rightarrow \frac{1}{\sqrt{3}}=\frac{20}{PB}\Rightarrow PB=20\sqrt{3}m\tan {60}^{\circ }=\frac{BC}{PB}\Rightarrow \sqrt{3}=\frac{h}{20\sqrt{3}}\Rightarrow h=\sqrt{3}\times 20\sqrt{3}=20\times 3=60m$

$\therefore$ height of plane$=60$m