Find the length to three significant digits of each arc intercept...

Question

Find the length to three significant digits of each arc intercepted by a central angle  in a circle of radius r. See Example 1.                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                       
 r = 15.1 in. , θ = 210°

Accepted Answer

Hello, today we're going to be determining the arc length of with the given central angle and the radius of a circle. Then we want to express our answer to two decimal places. So what we have is we have a circle. Now this circle has a central angle, theta the central angle theta is given to us as 240 degrees. And we are told that the radius of the circle is equal to 25.99 yards. We want to go ahead and use this information to determine the length of the arc that is formed by the inner angle. So how can we go about solving for the arc length of this circle? Well, we have an equation of arc length and the equation of the arm length is given to us as S is equal to R multiplied by the, this is where R represents the radius of the circle and the is the central angle in terms of radiance. Now, if we take a look at our central angle, the angle is given to us in terms of degrees. So we're going to have to change the given angle from degrees to radiance. In order to do that, we can take our angle theta which is 240 degrees and multiply it by the quantity pi divided by 180. Doing so will give us a central angle which is pi divided by 180. And this fraction will simplify to leave us with four pi divided by three. So this is going to be our angle theta in terms of pi and now that I mean in terms of radiance and now that we have our data in terms of radiance and the radius of the circle, we can use this information to find the arc length of the circle. So we have ss equal to the radius which is 25. yards multiplied by the central angle which is four pi divided by 3, 25.9 multiplied by four pi divided by three will leave us with 103.6 P divided by three yards. Now, at this point, I would recommend plugging in this value into a calculator if you do. So, we're going to end up with a very lengthy decimal. The arm length will approximately equal to 108.48966 and continuous yards. Now, what we're going to do is we're going to mo to round this decimal to two decimal places. So we're going to look at the number to the right of eight, this number is greater than five. So we're going to be rounding up 8 to 9. And once we do that, that will give us a final arc length of 108.49 yards. This will be the arc length that is created with the central angle. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 15.1 in. , θ = 210°

Key Concepts

Arc Length Formula

Central Angle

Significant Figures

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