Questions: Find the radian measure of the central angle θ given the radius r and the arc-length s transcribed by θ. r=10 in.; s=21 in.

Find the radian measure of the central angle θ given the radius r and the arc-length s transcribed by θ. r=10 in.; s=21 in.
Transcript text: Find the radian measure of the central angle $\theta$ given the radius $r$ and the arc-length $s$ transcribed by $\theta$. \[ r=10 \text { in.; } s=21 \text { in. } \]
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Solution

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Solution Steps

Step 1: Identify the given values

The problem provides the radius \( r = 10 \) inches and the arc length \( s = 21 \) inches.

Step 2: Use the formula for the central angle in radians

The formula to find the central angle \( \theta \) in radians is: \[ \theta = \frac{s}{r} \]

Step 3: Substitute the given values into the formula

Substitute \( s = 21 \) inches and \( r = 10 \) inches into the formula: \[ \theta = \frac{21}{10} \]

Final Answer

\[ \theta = 2.1 \text{ radians} \]

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