SOLUTION: Use trigonometry to find the measure of the arc cut off by a chord 12 cm long in a circle of radius 10 cm.

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Question 300074: Use trigonometry to find the measure of the arc cut off by a chord 12 cm long in a circle of radius 10 cm.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

We want to find the red arc at the top of this circle
of radius 10.



we draw in two 10 cm radii to the ends of the 12 cm chord



We need to find angle theta, which subtends
the red arc. We use the law of cosines, with our
calculator in radian mode.  If you haven't had the
law of cosines yet, we can do it by considering
two right triangles.  Post again if you need us to
do it that way.

cos%28theta%29=%2810%5E2%2B10%5E2-12%5E2%29%2F%282%2A10%2A10%29=0.28

theta=1.287002218radians

We use the arc length formula:

s=r%2Atheta=10%2A1.287002218=12.87002218cm

Edwin