 In this video, we provide the solution to question number six for the practice exam number one for math 1060 And we're asked to compute the length of the arc associated to the central angle of a circle where the circle has a radius of three centimeters and The measurement of the central angle is a hundred degrees now to compute arc length We're going to use the formula s equals r theta where s is the length of the arc R is the radius of the circle the length of that radius and theta is the measurement of the angle but that measurement does have to be in Radians the angle was given us in degrees. So we have to convert it to radians first So if theta equals a hundred degrees to convert it to radians We're gonna multiply by pi over 180 degrees. We want to simplify this fraction here Now be aware we do not have access to a calculator on this part of the test So we'll just have to do it by hand. We can see that a hundred and a hundred and eighty Both have a factor of ten because their last digit is a zero. You can cancel that out Notice that also that ten and eighteen have a common factor of two ten is two times five and Eighteen is two times nine so we can rewrite this angle in radians as five pi over nine That's the angle measure. So to compute the arc length We're gonna take three centimeters and times it by the five pi over nine radians You could take three times five and get 15 pi over nine centimeters But we do want this to be simplified notice, of course that three does go into nine You get that exactly three times and so we see the distance the length of the arc That is is gonna be five pi over three centimeters And so that causes us to select choice B as the correct answer