What is the length of a minor arc that is intercepted by a central angle whose measure is 50 degrees and the circle has a radius of 10?

Hello!

As you know, the length of an entire circumference of a radius `r` is `2 pi r,` and an entire circumference contains the central angle of 360 degrees.

Also the length of an arc is proportional to the measure of its central angle. The proportion is:

length of an arc with an angle `alpha` : length of an entire circumference = `alpha` : 360°,

or

length for angle alpha : `2 pi r` =...

Hello!

As you know, the length of an entire circumference of a radius `r` is `2 pi r,` and an entire circumference contains the central angle of 360 degrees.

Also the length of an arc is proportional to the measure of its central angle. The proportion is:

length of an arc with an angle `alpha` : length of an entire circumference = `alpha` : 360°,

or

length for angle alpha : `2 pi r` = `alpha` : 360°

(alpha is in degrees also).

Thus the length is `2 pi r * alpha/360,`  in our case it is  `(2 pi *10*50)/360=pi*25/9,` or approximately `8.73.`