Question

A circle has a radius of 34 centimeters. What is the measure of the central angle, in degrees, that intercepts an arc of length 145 centimeters? Round to the nearest degree. You must show your work to receive credit.

Answer 1

Answer: 244 degrees

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The formula we can use is

L = (a/360)*2*pi*r

where,

L = arc length

a = central angle in degrees

r = radius

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In this case, r = 34 and L = 145. We want to find the angle 'a'.

L = (a/360)*2*pi*r

145 = (a/360)*2*pi*34

145 = (a/360)*68pi

145*360 = a*68pi

52200 = a*68pi

a*68pi = 52200

a = 52200/(68pi)

a = 244.3496

a = 244