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Chapter 4: Problem 73

Find the length of the arc on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). Express arc length in terms of \(\pi .\) Then round your answer to two decimal places. (TABLE CAN NOT COPY)

Short Answer

Expert verified
The arc length \( s \) is rounded to two decimal places and, if possible, expressed in terms of \( \pi \). Unfortunately, without specific values for \( r \) and \( \theta \), a specific numerical answer cannot be provided at this time.

Step by step solution

01

Identify Knowns and Unknowns

From the problem statement, we can see that \( r \) (the radius of the circle) and \( \theta \) (the central angle) are known, while \( s \) (the arc length) is unknown. We want to solve for \( s \).
02

Apply the Formula for Arc Length

We make use of the formula \( s = r \theta \) to calculate the arc length. This formula allows us to find the length of a sector of a circle given the radius and central angle.
03

Compute the Arc Length

Substitute the respective values of \( r \) and \( \theta \) into the formula \( s = r \theta \) to evaluate for \( s \). This will represent the arc length.
04

Express in Terms of Pi and Round

If the value of \( s \) can be expressed in terms of \( \pi \), do so. Regardless, round this value to two decimal places to provide the required answer.

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