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Chapter 32: Problem 1049

What length of arc is subtended by a central angle of \(75^{\circ}\) on a circle \(13.7\) inches in radius?

Short Answer

Expert verified
The length of the arc subtended by a central angle of \(75^{\circ}\) on a circle with a radius of 13.7 inches is approximately 17.694 inches.

Step by step solution

01

Convert the central angle to radians

To convert a degree measure to radians, we can use the following formula: Radians = (Degrees * 蟺) / 180 For our problem, we have the central angle as 75 degrees. Therefore, Radians = (75 * 蟺) / 180
02

Simplify the expression

Now, simplify the expression to get the central angle in radians: Radians = (75 * 蟺) / 180 = (15 * 蟺) / 36
03

Calculate the arc length

Now that we have the central angle in radians, we can calculate the arc length using the formula Arc length = (central angle in radians) * radius: Arc length = ((15 * 蟺) / 36) * 13.7
04

Simplify and compute the result

Now, simplify and compute the result: Arc length = (15 * 蟺 * 13.7) / 36 鈮� 17.694 inches So, the length of the arc subtended by the central angle of 75 degrees in a circle with a radius of 13.7 inches is approximately 17.694 inches.

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