Question

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is ${30}^{\circ }$.

Answer 1

Let AB be the vertical pole and AC be 20 m long rope tied to point C.
In right $\Delta ABC$,

$sin{30}^{\circ }=\frac{AB}{AC}$
$\Rightarrow \frac{1}{2}=\frac{AB}{20}$
$\Rightarrow AB=\frac{20}{2}$
$\Rightarrow AB=10$
Thus, the height of the pole is 10 m.