Question

The 190° arc measures 25 mm. What is the diameter of the entire circle?

Answer 1

You can start by converting from degrees to radians and using the relation


`L=r\theta=\frac12d\theta`

Or just set up the proportion equation,


`\frac{\text{arc length}}{\text{circumference}}=\frac{25\text{ mm}}{180^\circ d}=(190^\circ)/(360^\circ)=\frac{\text{angle subtended by arc}}{\text{one revolution}}\implies d=\frac5{19}`