How do you find the length of an arc in a circle with a radius of 8 when the arc measures 45 degrees?

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To find the length of an arc in a circle, you can use the formula:

Arc Length = rac{ heta}{360} imes 2 ext{π}r

Where:

  • heta = angle of the arc in degrees
  • r = radius of the circle
  • π (Pi) ≈ 3.14159

In this case:

  • The radius (r) is 8.
  • The angle ( heta) is 45 degrees.

Now, plug these values into the formula:

Arc Length = rac{45}{360} imes 2 imes ext{π} imes 8

First, simplify the fraction:

rac{45}{360} = rac{1}{8}

Now substitute this back into the formula:

Arc Length = rac{1}{8} imes 2 imes ext{π} imes 8

Next, eliminate the 8 in the numerator and denominator:

Arc Length = rac{1}{8} imes 2 imes ext{π} imes 8 = 2 ext{π}

Now, if you want a numerical value, we can approximate it:

Using the value of π ≈ 3.14:

Arc Length ≈ 2 imes 3.14 = 6.28

So, the length of the arc with a radius of 8 and measuring 45 degrees is approximately 6.28 units.

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