# Math

posted by .

Given info:
arc length = 65 m
formula for arc length: s=rø
s = 2pi r

so to find the angle
would I put in 2pi(2300)= rounded to 14451

Then would I multiply: 65(360/14451)

if that is right, why would I divide by 360 and multiply by 65? Could someone explain

• Math -

The simplest way to find the angle is to use the formula:
s=rφ
Solve for φ and convert to degrees:
φ = (s/r) *(180/π)
= 65/2300 * (180/π)
= 1.619°

What is done above is to divide 65m by the circumference of the circle, and the convert the fraction of 360° to degrees. That is why some of the numbers cancel out in the end.

• Math -

ok, thank you!

• Math -

could you explain the cancellations?

• Math -

The circumference is
2πr = 2π*2300 = 4600π
the arc length is 65
arc-length/circumference = φ/360°
φ=(65/4600π)*360°
=1.619° (same as the other method).

Your procedure is to calculate them numerically to get 14451m (rounded) as the circumference.
then you multiply the fraction
(65/14451) by 360° (angle of a complete turn).
Really there is no cancellation required.

So
"Then would I multiply: 65(360/14451)"

"if that is right, why would I divide by 360 and multiply by 65? Could someone explain "
No you don't need to divide by 360 and multiply by 65 (unless you want to get back the circumference).

• Math -

I'm still a bit confused on how you get from s = rφ to arc length /circumference = φ/360

s = rφ
2πr = rφ

• Math -

s=rφ where φ is in radians.
To change from radians to degrees, we multiply by 180°/π, since π radians equal 180°.

For an angle a whole circle, it is 2π radians or 360°.
So 2πr is the circumference, where φ=2π. (we know this formula from elementary school, but did not know from where it came).

So
s = rφ
2πr = rφ
are the one and same formula, the first one for an angle of φ, and the second for φ=2π (or a complete circle).

Hope I made that clear. If not, feel free to post.

## Similar Questions

1. ### Math

It takes ten identical pices to form a circular track for a pair of toy racing cars. If the inside arc of each pair is 3.4 inches shorter than the outside arc, what is the width of the track?
2. ### math

Whats the difference between an arc [of a circle]'s length and measure?
3. ### maths

Im confused can any1 help me on this question ?
4. ### precalculus

The question is...find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Then it gives the radius r of 27 inches and an arc length s of 6 inches. How do I do that?
5. ### Trig

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.?
6. ### Math rem

2.Find the length of the arc in a circle if the radius of the circle is 24cm and the degree of the arc is 90o 3.Find the length of the arc if a circle if the degree if the arc is 120o and the length of the radius is 8cm. 4. A circle …
7. ### Math Arc Length

Find the arc length corresponding to an angle of a degrees on a circle radius of 4.9 Enter the exact answer. I put the arc length was 4.9api/180 got it wrong. Any help?
8. ### math

An angle of 1.8 radians at the center of the circle subtends an arc of length 23.4cm. Find: (a) The radius of the circle (b) The area of the sector enclosed by the arc and the radii.
9. ### Algebra

A tennis player's swing moves along the path of an arc. If the radius of the arc's circle is 4 feet and the power and the angle of rotation is 100 degrees, what is the length of the arc?
10. ### apex geometry

Hannah constructed two similar circles as seen in the image below. If the arc length of the larger circle is , which of the following would be true?

More Similar Questions