SOLUTION: Question is: if the radius of a circle is 8ft and the central angle is 5pi/4 find the intercepted arc length. I know that 5pi/4 equals 225 degrees and the diameter is 16ft but i

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Question 415035: Question is: if the radius of a circle is 8ft and the central angle is 5pi/4 find the intercepted arc length.
I know that 5pi/4 equals 225 degrees and the diameter is 16ft but im not sure how to set this equation up to figure the intercepted arc length.
thank you
Found 2 solutions by stanbon, jsmallt9:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Question is: if the radius of a circle is 8ft and the central angle is 5pi/4 find the intercepted arc length.
I know that 5pi/4 equals 225 degrees and the diameter is 16ft but im not sure how to set this equation up to figure the intercepted arc length.
----------------
arc length/circumference = central angle/360
-----
arc length = (16pi)[225/360]
----
arc length = (16pi)*0.625 = 10pi ft
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Cheers,
stan H.
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Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
A measure of a central angle, the length of its intercepted arc and the area of the sector formed are all proportional in the following way:

central angle length of arc area of sector -------------- = --------------- = --------------- 360 or 2 circumference total area

Your problem involves the central angle and the arc length so we will use just the first two fractions. And since the angle is given in radian measure we will use in the first denominator. So the proportion we will use is:

which simplifies to

Now we can solve for x. Cross Multiplying we get:

dividing by 8 we get:

This is an exact expression for the solution. If you want/need a decimal approximation, replace the with a decimal approximation (3.1415926...) and multiply by 10.