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Chapter 4: Problem 10

Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). (TABLE CAN NOT COPY)

Short Answer

Expert verified
The radian measure of the central angle (\( \theta \)) is obtained by dividing the length of the arc (\(s\)) by the radius of the circle (\(r\)), i.e. \( \theta = \frac{s}{r} \).

Step by step solution

01

Identify Known Values

Here, we are provided with the radius of the circle (\(r\)) and the length of intercepted arc (\(s\)). These are the known values in the problem.
02

Apply formulas for Arc Length

Using the formula for the relation between central angle in radians (\( \theta \)), arc length (\( s \)) and the radius (\( r \)), write down the formula \( \theta = \frac{s}{r} \).
03

Substitute and Solve

Substitute the known values of \(s\) and \(r\) into the formula to find the radian measure of the central angle. Use algebraic methods or a calculator where necessary to solve for \( \theta \).

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