Find the length of the arc on a circle of radius 10 feet intercep...

Question

Find the length of the arc on a circle of radius 10 feet intercepted by a 135° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.

Accepted Answer

Hello, today we're gonna be solving the following arc length problem. So we are told to calculate the length of an arc on a circle with a radius of 14 m, a central angle of 112 degrees intercepts the, the arc. We won't want to write the answer in terms of pi and in a decimal rounded to the nearest 100th. So let's go ahead and draw an image to help us solve this problem. So we have a section of a circle with a given angle inside the angle is given to us as 112 degrees. And we are told that the radius of the circle is 14 m long. We want to go ahead and calculate the length of the arc that is formed on the circle. So how do we go about doing that? Well, we're going to have to use the arc length formula. Now, the arc length formula is given to us as S is equal to R times theta S represents the arc length R represents the radius of the circle and theta represents the central angle. So we're going to need to use this formula in order to solve this problem. So based off of the image that we drew, we know that R is going to equal to 14 and we know that theta is given to us as 112 degrees. Now remember that the answer or the problem asks us to write the answer in terms of pi currently, our theta is given to us in degrees. So we're going to have to convert this angle from degrees to radiance. In order to do this, we can multiply 100 and 12 by pi over 80. Doing so is going to give us the value of 112 pie over 1 80. And this value is going to simplify to give us pi over 45. So this is going to be theta in the form of a radiant. So now that we have the two pieces of information we need to solve for the arc length, we can take our value of R and data and plug it into the arc length formula. Doing so is going to give us 14 multiplied by the quantity 28 pi over multiplying these values together is going to give us the value of 392 pi over 45. So the arc length in radiance is represented by 392 pi over 45 m. But we also want to convert this answer as a decimal rounded to the nearest 100th. If you were to plug in this value into a calculator and round the given decimal to the nearest 100th place, we get an estimated value of 27. m. And these are going to be the answer to the arc length problem. And with that being said, the answer to this problem is going to be B 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 of the arc on a circle of radius 10 feet intercepted by a 135° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.

Key Concepts

Arc Length Formula

Conversion from Degrees to Radians

Circumference of a Circle

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