SOLUTION: A circle has a radius of 12 mm. A central angle measuring 7pi/6 radians intercepts n arc. What is the length of the arc? I have used the formula s=rθ. 12*7pi/6 = 14pi = 43.

Algebra ->  Trigonometry-basics -> SOLUTION: A circle has a radius of 12 mm. A central angle measuring 7pi/6 radians intercepts n arc. What is the length of the arc? I have used the formula s=rθ. 12*7pi/6 = 14pi = 43.      Log On


   

Question 1116761: A circle has a radius of 12 mm. A central angle measuring 7pi/6 radians intercepts n arc. What is the length of the arc?
I have used the formula s=rθ. 12*7pi/6 = 14pi = 43.98 mm. For some reason, this doesn't seem right to me.

Thank you for your time
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
.
Arc length = r%2Atheta = 12%2A%287pi%2F6%29 = 12%2A%28%287%2A3.14%29%2F6%29 = 43.96 mm.

Solved.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The circumference, +C+ is:
+C+=+2%2Api%2Ar+
+r+=+12+ mm
+C+=+2%2Api%2A12+
+C+=+24pi+
-----------------------------
There are +2pi+ radians of arc in a circle
+%28%28+7pi+%29%2F6+%29+%2F+%28+2pi+%29+=+a+%2F+%28+24pi+%29+
Multiply both sides by +2pi+
+%28+7pi+%29%2F6+=+a%2F12+
Multiply both sides by +6+
+7pi+=+a%2F2+
+a+=+14pi+
The length of the arc is 14pi mm
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This seems about right. One-half of the circumference
would be +24pi%2F2+=+12pi+
And +7pi%2F6+ is a little more than half of +C+
so, +14pi+ seems gight