Video Transcript
A squash player moves in an arc-shaped path with the circle of radius 1.6 meters with a rotation angle of 71 degrees. Find the length of the arc that the player makes giving the answer to one decimal place.
So what I’ve done first here is drawn a sketch. So we’ve got something here that is basically a sector of a circle. And so we have the central angle of 71 degrees, we have radius of 1.6 meters, and we want to find the arc length. And to find the arc length, we have a formula. And that formula is 𝜃 over 360 multiplied by two 𝜋𝑟. It could be multiplied by 𝜋𝑑 as well. And that’s because the radius is half the distance of the diameter.
Okay, so why have we got this formula? Well, it comes from the formula for the circumference of a circle, which is equal to two 𝜋𝑟 or 𝜋𝑑. And that’s because the 𝜃 over 360 gives us a fraction of our circle, which the arc length is. It’s a fraction of the circumference because what we have is our angle or our central angle over 360 because 360 is the total angle or total number of degrees in a circle.
Well, if we substitute in the values we’ve got, we’re gonna have 𝑙. So our arc length is equal to 71 over 360 multiplied by two multiplied by 𝜋 multiplied by 1.6, which is gonna give an answer of 1.98269403. But this wasn’t the answer we were looking for because if you look at the question, it says it wants the answer to one decimal place. So if we round to one decimal place, what we’re gonna get is 2.0 meters. And that’s gonna be the arc length that the player makes.
