Question

Can someone help me with this? I'll type in my problem

Answer 1

I can help. :)

Answer 2

Question:
What is the arc measure of an arc with length 4.189 cm and radius equal to 3 cm.

my guess answer:
(4.189/360) * 2π(3) ≈
(1/90) * 2π(3) ≈
(1/90) * 6π =
(1/90) * 18.85 ≈
0.21

I am having trouble because the formula I learned in my lesson goes like this:
[(arc measure)/360] * C
C is the circumference, but the arc measure that was mentioned in the lesson was in degrees. So I'm not sure if I made a mistake, because the question doesn't give the measure of the arc in degrees, but in cm. I really don't think this is done right. Help?

Answer 3

Of course, I'll help.

Answer 4

4.189/[2 π 3] = x/360
6 π x = 360 *4.189

x = 80.0 degrees approx

I think you wanted the central angle measure of the angle that subtends that arc.

Answer 5

So does this mean the arc measures 80 degrees?

Answer 6

Yes, did you have answer choices that came with?

Answer 7

No, I have to write it myself.

Answer 8

I see. give me a few minutes, I need to check my work over.

Answer 9

OK. Can you also give me the formula you used to find that angle measure?

Answer 10

Ohhh, hah. Yea, I see what I did wrong. Divide 4.189 / 3 to get the angle in radians, it's about 1.396
Multiply by 180/pi to get the angle in degrees, it's about 80

If the radius is 7, the area of the entire circle is pi * 7^2 = 49*pi =~ 153.938
So the angle (in degrees) is 360 * 38.485 / (49*pi) which is almost exactly 90 degrees
So the arc length is approximately 90/360 times the circumference of the circle, i.e.:
(90/360) * 2*pi*7 =~ 10.9957