SOLUTION: the measure of the central angle of a circle is 70 and arc AC is 3 meter,what is the measure of the radius?

Question 945586: the measure of the central angle of a circle is 70 and arc AC is 3 meter,what is the measure of the radius?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the arc length of a circle with a central angle of 70 degrees is equal to 70/360 * 2 * pi * r.

since the arc length is equal to 3 meters, the equation becomes:

3 = 70/360 * pi * r

solve for r to get r = (3 * 360) / (70 * 2 * pi).

that would make the radius equal to 2.455533408.

to see if this is correct, find the circumference of the circle with a radius of 2.455533408 and then find the length of an arc that has a central angle of 70 degrees.

the circumference of the circle is equal to 2 * pi * r which becomes equal to 2 * pi * 2.455533408 which is equal to 15.42857143.

the length of the arc is equal to 70 / 360 * 2 * pi * r.

since 2 * pi * r is equal to 15.42857143, then the equation becomes:

the length of the arc is equal to 70 / 360 * 15.42857143 which is equal to 3.

that confirms that the solution is correct and that the length of the radius is equal to 2.455533408.
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