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

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: 1 meter
Arc Length, s: 600 centimeters

Accepted Answer

Welcome back. I am so glad you're here. We're told the arc of a circle has a length of 920 centimeters. Calculate the central angle in radiance that intercepts the arc. If the radius of the circle is two m, our answer choices are answer choice. A 23 divided by five radians. Answer choice B 19 divided by five radians. Answer choice C 27 divided by eight radians and answer choice D 17 divided by four radians. All right. So what do we know? And what formula are we going to use? Well, let's start with the formula we recall from previous lessons that theta our central angle equals S which is the length of the arc divided by R, which is the radius. So theta is the central angle that's in gradients. And that's what we're looking for. That's what we're trying to calculate. S is our length of the arc. And here we're told that the length of the arc of our circle is 920 centimeters. And then finally, r that's the radius. We're told that the radius of our circle is two m. So we will be taking, we're trying to find data. We will be taking S which is centimeters and dividing that by R which is two m. However, we are not in the same unit in our numerator and our denominator. So we can do some unit conversion here. We could go to meters or to centimeters, either one. But what we go, what we'll do is we know that for every meter, for every meter, there is 100 centimeters. So we can use one m in the numerator and 100 centimeters in the denominator. And when we do that, our centimeters will cancel out and our meters will cancel out and that will leave just the radiance from our data. So in the numerator 920 multiplied by one is 920 that's divided by two, multiplied by 100 which is 200. And when we simplify this, this will reduce to 23 divided by five and that is in ingredients. So our answer for that central angle is 23 divided by five radians. We look at our answer choices and this matches with answer choice. A 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: 1 meter Arc Length, s: 600 centimeters

Key Concepts

Radian Measure

Arc Length Formula

Unit Conversion

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