Find the radius r of the circle if an arc of length 20 cm on the circle subtends a central angle of 50°. (Round your answer to two decimal places.)

Question

I would really appreciate if someone can tell me step by step with answer. I am really struggling with this section of homework and I need to see a full problem in order to understand it.

Answer 1

Circumference = C = 2(pi)(r)

r = C/(2pi)

Circumference = Arc length (360/central angle)

C= 20(360/50) = 144 cm

Therefore:

r= 144/(2pi)

r= 22.92 cm

Answer 2

1° = (π/180)^r

50º = (50π / 180)^r

50° = (5π / 18)^r

20 cm = (5π / 18)^r

(20 cm)(18 / 5π) = r