Home/Class 10 Math Chapter List/11. Some Applications of Trigonometry/# A circus artist is climbing a (20m) 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^{o}) (see figure).

A circus artist is climbing a \(20m\) 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 \(30^{o}\) (see figure).

\(10\ m\)

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In the given figure, AB be the height of the pole and\(AC=20m\) be the length of rope which is tied from the top of the pole.

We have to determine the height \(AB=?\)

\(\ln \Delta ABC,\)

\(\sin 30^{\circ }=\frac {AB}{AC}=\frac {AB}{20}\)

\(\Rightarrow\) \(\frac {1}{2}=\frac {AB}{20}\) [\(\because \sin30^{\circ}=\frac{1}{2}\)]

\(\Rightarrow\) \(AB=\frac {20}{2}=10m\)

Hence, the height of the pole is \(10m\)

We have to determine the height \(AB=?\)

\(\ln \Delta ABC,\)

\(\sin 30^{\circ }=\frac {AB}{AC}=\frac {AB}{20}\)

\(\Rightarrow\) \(\frac {1}{2}=\frac {AB}{20}\) [\(\because \sin30^{\circ}=\frac{1}{2}\)]

\(\Rightarrow\) \(AB=\frac {20}{2}=10m\)

Hence, the height of the pole is \(10m\)

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