In Exercises 7–12, find the radian measure of the central angl...

Question

In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 10 inches Arc Length, s: 40 inches

Accepted Answer

Welcome back. I am so glad you're here. We are told an arc of a circle has a length of 240 m. Calculate the central angle in radiance that intercepts the arc. If the radius of the circle is 40 m, our answer choices are answer choice A six pi radiance answer choice B eight radiant answer choice C six radiant and answer choice D radiant. All right. So to find the central angle, we recall from previous lessons that we have a formula for that, we know that theta theta represents the central angle. That's what we're trying to find. And it is in radiance, theta is equal to S where S is the length of the arc, an S is divided by R where R is the radius. And we know some of these already the central angle. That's what we're trying to find the length of the arc. We're told in the problem that that is 240 m. And the radius of the circle we're told in the problem that that is m. So we can plug in for S and for R in the numerator for S, we have 240 m that's divided by in the denominator for r we have 40 m and our meters here cancel out, which is great as we said that theta is already measuring in radiance. So when we take 240 divided by 40 that gives us six and it is six radiance. Now we look at our answer choices and six radiance matches with answer choice. C however, you might be wondering why is it not answer choice? A if you're wondering that usually when we're talking about Radians, there's some sort of pie there. So it might be really tempting to choose that one. But pi really represents a number. And so if we had six pi radiant, that would be six multiplied by 3.1415 and so on. So that's almost 18. So if that was our answer, we'd be talking about 18, approximately radiance which is far different from six radiant. So it means something very different. All right. So our answer choice is answer choice. C well done. We'll catch you on the next one.

In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 10 inches Arc Length, s: 40 inches

Key Concepts

Radian Measure of an Angle

Relationship Between Arc Length, Radius, and Central Angle

Units and Conversion in Trigonometry

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