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: 6 yards
Arc Length, s: 8 yards

Accepted Answer

Welcome back. I am so glad you're here. We're told that the arc of a circle has a length of 148 ft. Calculate the central angle in radiance that intercepts the arc. If the radius of the circle is 80 ft. Our answer choices are answer choice. A 35 divided by 19 radians. Answer choice B 20 divided by 33 radians. Answer choice C 11 divided by 21 radians and answer choice D 37 divided by 20 radians. All right. So we need to calculate the central angle. Well, we recall from previous lessons that the central angle which is expressed in theta and is already in radians is equal to S where S is the length of the arc divided by R where R is the radius. And we know some of these, the central angle. That's what we're looking for. The length of the arc we're told in the problem is 148 ft and the radius we're told in the problem is 80 ft. So we can plug those in, plugging in. For s in the numerator, we have 148 ft and that's divided by the r in the denominator is 80 ft and those feet cancel each other out, which is great. And as we said that theta is already in radiance. So when we take 148 divided by that's going to simplify 2 37 divided by 20. And that's in radiance and there's our answer 37 divided by 20 radians. We look at our answer choices and this matches with answer choice D 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: 6 yards Arc Length, s: 8 yards

Key Concepts

Radian Measure

Arc Length Formula

Central Angle

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