In Exercises 71-74, find the length of the arc on a circle...

In Exercises $71-74,$ find the length of the arc on a circle of radius $r$ intercepted by a central angle $\theta .$ Express arc length in terms of $\pi .$ Then round your answer to two decimal places. $$\begin{array}{ll}{\text { Radius, } r} & {\text { Central Angle, } \theta} \\ {9 \text { yards }} & {\theta=315^{\circ}}\end{array}$$

In Exercises $71-74,$ find the length of the arc on a circle of radius $r$ intercepted by a central angle $\theta .$ Express arc length in terms of $\pi .$ Then round your answer to two decimal places.
$$\begin{array}{ll}{\text { Radius, } r} & {\text { Central Angle, } \theta} \\ {9 \text { yards }} & {\theta=315^{\circ}}\end{array}$$

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Key Concepts

Arc Length Formula

This is a formula used to calculate the distance along the circumference of a circle that is intercepted by a central angle. The formula, s = r?, where s is the arc length, r is the radius, and ? is the angle in radians, is essential for solving problems involving parts of circles.

Conversion Between Degrees and Radians

Since many angle measures are given in degrees but the arc length formula requires the angle in radians, it is important to convert degrees to radians by multiplying by ?/180. This conversion is critical for ensuring the correctness of the calculation.

Expressing Answers in Terms of ?

In many problems, especially those involving circles, the answer is expressed in terms of ? to maintain exactness and clarity. Expressing the answer like this avoids approximations until a final numerical value is necessary.

Rounding to Specified Decimal Places

When a problem requires a final answer rounded to a certain number of decimal places, it's important to apply appropriate rounding techniques after performing the necessary calculations to ensure the final result meets the specified precision.

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