A circus artist is climbing a $ 20 \mathrm{~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} $.

Given:

Length of the rope$=20\ m$.

The angle made by the rope with the ground level is \( 30^{\circ} \).

 To do:

We have to find the height of the pole.

Solution:

Let AB be the height of the pole and AC the length of the rope.

Angle made by the rope with the ground $\angle BCA=30^o$

Therefore,

$sin30^o=\frac{AB}{AC}$

$\frac{1}{2}=\frac{AB}{20}$

$AB=\frac{20}{2}$

$AB=10\ m$

The height of the pole is $10\ m$.