SOLUTION: If the length of an arc is 18(pi) meters and the central angle measures 75 degrees, find the radius of the circle.

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Question 309472: If the length of an arc is 18(pi) meters and the central angle measures 75 degrees, find the radius of the circle.
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If the length of an arc is 18(pi) meters and the central angle measures 75 degrees, find the radius of the circle.
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1st: Find the circumference.
c/360 = (18pi)/75
c = 360[18pi/75]
c = 86.4pi meters
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Now, find the radius:
2(pi)r = 86.4pi
r = 43.2 meters
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Cheers,
Stan H.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Length of the arc is 18 * pi meters.
The central angle measures 75 degrees.

The circumference of a circle is equal to 2 * pi * r

The length of an arc of a circle is equal to d/360 * 2 * pi * r

d is the degrees of the central angle.

If the angle is 360 degrees, then this formula becomes the length of the arc is equal to the circumference of the circle is equal to 2 * pi * r.

Sinc d = 75, then this formula becomes:

75/360 * 2 * pi * r = 18 * pi

Divide both sides of the equation by pi to get:

75/360 * 2 * r = 18

Simplify to get:

.41666666667 * r = 18

Divide both sides of the equation by .41666666667 to get:

r = 18/.l41666666667 = 43.2 meters.

The radius of the circle is equal to 43.2 meters.

This makes the circumference of the circle equal to 2 * pi * 43.2 = 86.4 * pi meters.

This makes the length of the arc of a central angle of 75 degrees equal to 75/360 * 86.4 * pi = 18 * pi meters