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A gymnast has a routine in which he sways back and forth on a high bar, making an arc that measures 135 deg. As he swings, the bottom of his shoes create an arc that measures 9 feet. At the conclusion of his routine, he swings completely around for one full circle around the bar. What is the circumference of that circle (answer in feet)?
Answer is 24.
Solution: A circle measures 360 deg. Find what portion a 135 deg arc is of a circle and then use that information to create a proportion. We get:
135/260 which can be reduced to 3/8.
So, 3/8 = 9 feet/x feet,
or 3/8 = 9/x,
or, 3x = 72
or, x = 24