A circle has a radius of 19 feet find the radian measure of the central angle theta that intercepts an arc of length 16 ft.

Answer 1

The big idea between using radians to measure angles is that you are using the radius to measure how far you've moved around the circle.

For any circle, the circumference i.e. the distance around the circle is 2πr where r is the radius. So there are 2π radius lengths around a circle. There are 2π radians in a circle.

In the above example, the radius is 19 feet and the ac length is 16 feet.. So the central angle measures 16/19 radians.

Answer 2

s = rς, so ς = s/r; so ς = 16/19