Problem

A circle has a radius of $11 \mathrm{~cm}$. Find the radian measure of the central angle $\theta$ that intercepts an arc of length $5 \mathrm{~cm}$. Do not round any intermediate computations, and round your answer to the nearest tenth. \[ \theta= \] radians

Solution

Step 1 :The radian measure of a central angle is given by the formula \(\theta = \frac{s}{r}\), where \(s\) is the length of the arc and \(r\) is the radius of the circle.

Step 2 :In this case, \(s = 5 \mathrm{~cm}\) and \(r = 11 \mathrm{~cm}\).

Step 3 :We can substitute these values into the formula to find \(\theta\).

Step 4 :\(\theta = \frac{s}{r} = \frac{5}{11} = 0.5\)

Step 5 :Final Answer: The radian measure of the central angle \(\theta\) that intercepts an arc of length \(5 \mathrm{~cm}\) in a circle with a radius of \(11 \mathrm{~cm}\) is \(\boxed{0.5}\) radians.

From Solvely APP
Source: https://solvelyapp.com/problems/19843/

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