Question

If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc?

216 degrees

270 degrees

288 degrees

(No picture/diagram is with the question)

Answer 1

@Nnesha

Answer 2

@hero

Answer 3

Look at the two circles below.

If we take two circles with different radii but having the same measure for their central angle, we get two arcs that have the same degree measure:
m = 60 and m = 60.

We are now going to be concerned about the length of arcs. Observation seems to tell us that the length of is greater than the length of . To find the length of an arc, we must find what portion of the circumference of the circle it is and then multiply the circumference by that fractional part. In dealing with length of arcs, an entire circle may conveniently be considered an arc of degree measure 360. We can then tell what fractional part of the circle our arc is: m The length of arc AB is times the circumference of the circle.

Since the circumference of a circle is 2 r, the length of .

In order to find out the measure of an arc length, we will first find the circumference of the circle, then multiply that number by the fractional part represented by the arc. For example, if the circumference was 4 and we wanted to know the length of an arc with a central angle of 90 degrees, we would do the following:

This should make some intuitive sense. Since the entire circumference of the circle is 4 an arc with central angle of 90 degrees (1/4 of the circle) should be ¼ of the circumference.

Model 1:

Find the exact length of a 60 arc in a circle of radius 6".

Solution:

1 - Plug values into length of arc formula:

2 - reduce the fraction, multiply 2 and 6
3 - Simplify: 2

Model 2:

Find the approximate length of a 90 arc in a circle of radius 14 ft. (Use = )

Solution:
1 - Plug values into length of arc formula:


2 - Reduce fraction and multiply 2 and 14: (1/4)(28)()

3 - Simplify by canceling out (1/28) and 28: 22 ft

Answer 4

these are the circles:

Answer 5

hmm now i'm confused
which one is your question isn't that If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc?
?

Answer 6

yes, all the other stuff is what is given to me in the lesson

Answer 7

okay so what's the formula to find the length of arc ?

Answer 8

Let me look through the lesson again

Answer 9

okay :-)

Answer 10

I was looking at this part of the lesson

"Find the exact length of a 60 arc in a circle of radius 6".
Solution:
1 - Plug values into length of arc formula:
2 - reduce the fraction, multiply 2 and 6
3 - Simplify: 2"
I was thinking since I don't have the measurement of the arc maybe I should reverse it in order to find the Arc measurement?

Answer 11

are you asked for the measure of the angle?

Answer 12

It's asking for the measurement of the arc, so yes.

Answer 13

length of an arc formula is