Arc length is distance along the circumference of a circle.\u00a0 Following a 360\u00b0 angle, you of course travel the entire circumference, which is 2\u03c0r, r being the radius.<\/p>\n
What is you’re traveling less the 360\u00b0?\u00a0 How can you calculate the corresponding arc length?<\/p>\n
Example:\u00a0 Calculate the arc length of a 110\u00b0 angle on a circle of diameter 15 cm.<\/em><\/p>\n Solution: First, realize that half the diameter is the radius. Therefore, the radius of this circle is 7.5cm.<\/p>\n Next, set up the following proportion:<\/p>\n 110\/360=x\/(2π7.5)<\/p>\n Next, we invoke the old “cross multiplication” trick described here<\/a>. It yields<\/p>\n 360x=110(2π7.5)<\/p>\n Dividing both sides by 360, we get<\/p>\n x=110(2π7.5)\/360=14.4cm<\/p>\n Apparently the arc length, if we only traverse 110\u00b0, is 14.4cm. Given that the arc length would be 2π(7.5)=47.1cm for the entire circle, our answer makes sense. 110 is just under a third of 360; correspondingly, 14.4cm is just under a third of 47.1cm.<\/p>\n I’ll be covering another method for arc length soon. Cheers:)<\/p>\n