$\"\"$

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Draw a diagram in which the ride is swinging in a $\"\"$ arc to a maximum height of $\"\"$ .

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Include a horizontal in the diagram, as shown.

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$\"\"$

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The tower is $\"\"$ .

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The distance from the maximum height of the ride to the horizontal is $\"\"$ .

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So, the length of the side opposite the $\"\"$ angle in the right triangle shown is $\"\"$ .

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An acute angle measure and the opposite side length are known, so the sin function can be

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used to write an expression for the length of the pendulum $\"\"$ .

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$\"\"$

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$\"\"$

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Use the fifth partial sum of the power series for sin to find $\"\"$ .

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Fifth partial sum of power series for $\"\"$ :

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The power series representing $\"\"$ is given by

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$\"\"$ .

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Converting to radians, $\"\"$

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Therefore $\"\"$ .

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$\"\"$ .

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$\"\"$

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Find the value of $\"\"$ :

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$\"\"$

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Therefore the length of the pendulam is $\"\"$ .

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$\"\"$

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The length of the pendulam is $\"\"$ .