A circular arc of length 16 ft subtends a central angle of 25°. How do you find the radius of the circle?

1 Answer
Jul 4, 2016

Consider the following diagram

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The formula for arc length is #s = theta xx r#, where #r# is the radius, #theta# is the center angle in radians and #s# is the arc.

We can convert #25˚# to radians using the conversion factor #pi/180#.

#theta" in radians" = 25 xx pi/180 = (5pi)/36#

Now, solving for #r# in the formula we have #s/theta = r#

#16/((5pi)/36) = r#

#(36 xx 16)/(5pi) = r#

#36.67 = r#

The radius measures 36.67 feet.

Hopefully this helps!