How to Find the Arc and Length of a Chord

The Pythagorean theorem can find the length of any side of a right triangle.
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An arc length and its corresponding chord are attached at their ends. An arc length is a measured segment of a circle's circumference. The chord is the line segment that runs through the circle from each endpoint of the arc length. You can calculate the arc length and the length of its chord through the circle's radius and the central angle, or angle that lies under the arc.

    Find the radian measurement of the central angle and the radius length. For this example, let the central angle be 0.75 radians and the radius be 5. Convert the central angle from degrees to radians with a converter like the one at University of Texas' Bureau of Economic Geology (see Resources).

    Multiply the central angle by the radius to calculate the arc length. With this example, 0.75 multiplied by 5 equals 3.75 radians.

    Divide the central angle by 2, and calculate its sine in radians with your calculator. With this example, 0.75 divided by 2 equals 0.375, and the sine of 0.375 is approximately 0.366 radians.

    Multiply the sine of the last step by the radius. With this example, 0.366 multiplied by 5 equals 1.83.

    Double the product of the prior step to calculate the chord length. Concluding this example, 1.83 multiplied by 2 equals 3.66. The chord length measures 3.66.

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