How to Calculate Radius of Arc Using the Delta Angle
According to "Math Open Reference," a website that specializes in the definitions and etymology of mathematical terms, an arc is "a portion of the circumference of a circle" that is designated by two points on the circle's circumference. The angle that is formed by connecting a straight line, called a radius, from these points to the circle's center is called the arc's delta angle. There is a relationship between an arc's length, delta angle and radii that lets you to determine one if you know the values of the other two, allowing you to use the delta angle to determine the arc radius if needed.
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Instructions
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Multiply the delta angle by pi (3.141592654) and divide the resulting number by 180 to convert the delta angle from degrees to radians. For example, a delta angle that measured 45 degrees would be multiplied by pi, resulting in 141.37. This number divided by 180 gives you an angle that measures 0.7853 radians.
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Rewrite the equation "angle measured in radians * radius = arc length" as "radius = arc length/angle measured in radians." The arc length value is necessary in order to determine the radii value for the arc; it is impossible to determine any of the three values in the equation without the other two. An equation that asks you to find the arc radius using the delta angle will also supply you with the arc length. For the example, let the arc length equal 5.
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Plug the values for the angle measured in radians and the arc length into the equation. The resulting answer will be the arc radius. For the example, the equation is radius = 5/0.7853. When calculated, the resulting radius length is 6.367.
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