00:01
My first problem, i am told that i have a central angle of 50 degrees, and the diameter of my circle is 16 meters.
00:19
To find the arc length, the formula is theta times r, but theta in all of these, theta must be in radians.
00:36
Anytime you plug theta directly into a formula, it must be in radiance.
00:42
So the first thing i'm going to do is convert 50 degrees into radiance by multiplying by pi over 180.
00:51
And that's going to give me 5 pi over 18.
00:55
So that's theta.
00:57
My radius is going to be half the diameter.
01:00
So my radius is 8 meters.
01:03
That means my arc length is going to be theta 5 pi over 18 times 8 so that's going to give me 40 pi over 18 or 20 pi over 9 and the unit of measurement is meters if you need an approximation you can just multiply 20 times pi and divide that by 9 and and you'll get approximately 6 .98 meters.
01:46
I move to the second problem and use another color so you can tell them apart.
01:51
This time i want to find the angle in degrees corresponding to an arc.
01:57
So in this case i have the arc and that is 7 centimeters if the radius is 4 centimeters.
02:09
Okay.
02:10
So again, same form.
02:12
Formula, theta times r, but this time i want to find theta.
02:18
Theta is going to be arc length divided by radius.
02:23
So 7 divided by 4.
02:26
That's radians.
02:30
I want to convert that to degrees by multiplying by 180 degrees over pi.
02:39
So 7 times 180 divided by 4...