Question

Two pillars of equal height stand on either side of a roadway which is 180 meters wide. The angle of elevation of the top of the pillars are ${60}^{\circ }$ and ${30}^{\circ }$ at a point on the roadway between the pillars. Find the height of the pillars and the position of the point.

Answer 1

R.E.F.Image.

In $△ABO,tan{60}^{\circ }=\frac{h}{x}$

$h=\sqrt{3}x\cdots \left(i\right)$

In $△DCO,tan{30}^{\circ }=\frac{h}{180-x}$

$180-x=h\sqrt{3}$

$180-x=3x$

$\Rightarrow 4x=180\Rightarrow x={45}^{\circ }m$

$\therefore OB=45m$

$OC=135m$

$h=\sqrt{3}x$

$=\sqrt{3}\times 45$

$h=45\sqrt{3}m$