Question

A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is ${30}^{\circ }$.

Answer 1

The figure above represents the given situation.
From the given firgure,
$cos{30}^{\circ }=\frac{BC}{AC}\Rightarrow BC=cos{30}^{\circ }\times AC=\frac{\sqrt{3}AC}{2}=\frac{30\sqrt{3}}{2}=15\sqrt{3}m$