Find the length s of the arc that subtends a central angle of measure 80° in a circle of radius 12 m. (Round your answer to two decimal places.)

Question

I am really struggling with these types of problems on my homework. None of the tutors have given me a full answer, I would really appreciate if someone can tell me step by step and give the answer so I can understand it.

Answer 1

Think of these questions as finding a part of the circumference. If you were asked to find the arc length for a central angle of 180 degrees that would be half the circle. In other words take the angle and divide by 360. You would get 180/360 = 1/2.

If the central angle was 90 degrees you would get 90/360 = 1/4.

I use these example because they are easier to understand.

Now for your problem you would do 80/360 = 2/9 ( I suggest reducing this fraction first )

Now multiply by 2 pi r (the formula for the circumference of a circle) to get 2/9 x 2 x pi x 12 = 16.76m

Answer 2

s = 2(pi)r (central angle/360)

s= 2(pi)(12)(80/360)

s - 16.76 m