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EXAMPLE 5 Find arc lengths to find distance TRACK The curves at the ends of the track shown are 180° arcs of circles. The radius of the arc for a runner on the red path shown is 36.8 meters. About how far does this runner travel to go once around the track? Round to the nearest tenth of a meter. SOLUTION The path of a runner is made of two straight sections and two semicircles. To find the total distance, find the sum of the lengths of each part.

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EXAMPLE 5 Find arc lengths to find distance = 2(84.39) + 2 2π 36.8 1 2 ≈ 400.0 meters The runner on the red path travels about 400 meters. ANSWER

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GUIDED PRACTICE for Example 5 6. In Example 5, the radius of the arc for a runner on the blue path is 44.02 meters, as shown in the diagram. About how far does this runner travel to go once around the track? Round to the nearest tenth of a meter. about 445.4 meters ANSWER

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Warm-Up Exercises Simplify the expression. ANSWER 1 8 3π3π 2. 120 360 (9π) 1. 45 360.

Warm-Up Exercises Simplify the expression. ANSWER 1 8 3π3π 2. 120 360 (9π) 1. 45 360.

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