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 $30 °$.

Question

A ladder 14 m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, then the height of the wall is:

Answer 1

A circus artist is climbing a 20 m long rope,
The figure indicates that AB represents the pole.
In triangle ABC:

$\frac{AB}{AC} = Sin 30^{\degree}$

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

$AB = \frac{20}2 = 10$

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

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 \(30 °\).