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 $10\ m$.
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