Question

What is the measure of the central angle of a circle with radius 15 ft that intercepts a 10 ft arc?

Answer 1

s = r(theta), where (theta) represents the central angle in radians (not degrees)

Here,

10 ft = (15 ft)(theta), or (theta) = 10/15 = 2/3 or 0.66667 radian

Answer 2

“thecircumference of a circle equals 2*pi*r, so
the circumference of the circle with radius 5 is
2*5*pi = 10pi
the ratio of the arc intercept to the circumference is equal to the ratio of the central angle of the intercept to 360 degrees (or 2*pi in radian units)
in our case
2/10*pi = x/2*pi, where x is the measure of the central angle
cross multiply and we get
4*pi = 10*pi*x
x = 0.4 radians which equals 22.92 degrees”