Question

The accompanying diagram shows the path of a cart traveling on a circular track of radius 2.40 meters. The cart starts at point A and stops at point B, moving in a counterclockwise direction. What is the length of minor arc AB, over which the cart traveled, to the nearest tenth of a meter?

Answer 1

when you have a circumference that has a radio of 1 unit we can say that 360° are going to be 2pi, or 180° is pi.

the formula for the arclength will be

`S=r\Theta`

now we have to pass the 165° to radians, and that is why we use the 180°=pi

`\begin{gathered} 180=\pi \\ 165=x \\ x=(165)/(180)\pi=(11)/(12)\pi \end{gathered}`

now that you have the angle in radians, multiply it by the radio.

`\begin{gathered} S=2.40\cdot((11)/(12)\pi) \\ S=(11)/(5)\pi\approx6.9m \end{gathered}`