a circle has a central angle of 60 deg which sebtends an arc of 30 inches find the radius?

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a circle has a central angle of 60 deg which sebtends an arc of 30 inches find the radius?

show the steps please

2007-02-06 14:23:05 · 3 answers · asked by k 1 in Science & Mathematics ➔ Mathematics

3 answers

60 deg will give an arc which is 1/6th of the full circumference.

2 pi r = full circum = 6 * 30
r = 180/2pi = 90/pi inches.

2007-02-06 14:29:27 · answer #1 · answered by astatine 5 · 0⤊ 0⤋

The angle in radians times the radius is the arc, so.
60*pi/180=pi/3 radians
r=30/(pi/3)=90/pi inches

2007-02-06 22:29:57 · answer #2 · answered by Anonymous · 0⤊ 0⤋

60 degrees is 1/6 of a full circle. Therefore, circumference of the full circle is 6 x 30" = 180".
Circ. = 2 pi radius; r = circ. / 2 pi; = 180 / 44 / 7; = (7 x 180)/ 44;
Radius = 28.63..."

2007-02-06 22:32:18 · answer #3 · answered by Richard S 6 · 0⤊ 0⤋