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Jabar goes to the playground to play on the swings. The length of each swing is 1.75 m.Jabar decides to swing higher. If the distance traveled on one swing is 3.5 m, what would be the central angle in degrees? Give your answer to the nearest degree.

Question

Jabar goes to the playground to play on the swings. The length of each swing is 1.75 m.Jabar decides to swing higher. If the distance traveled on one swing is 3.5 m, what would be the central angle in degrees? Give your answer to the nearest degree.

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Solution

The central angle can be calculated using the formula for the circumference of a circle, which is C = 2πr, where r is the radius of the circle. In this case, the length of the swing is the radius of the circle, which is 1.75 m.

  1. First, calculate the circumference of the circle using the given radius: C = 2πr = 2π(1.75 m) = 11 m (approximately)

  2. Next, find out what fraction of the circle's circumference is covered in one swing. This is done by dividing the distance traveled on one swing by the total circumference: Fraction = Distance / Circumference = 3.5 m / 11 m = 0.318 (approximately)

  3. To find the central angle, multiply this fraction by 360° (since there are 360° in a full circle): Central Angle = Fraction * 360° = 0.318 * 360° = 114° (approximately)

So, the central angle is approximately 114°.

This problem has been solved

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