Questions: In a circle with a 120 km radius, how long is an arc associated with an angle of 4.4 radians?

In a circle with a 120 km radius, how long is an arc associated with an angle of 4.4 radians?
Transcript text: In a circle with a 120 km radius, how long is an arc associated with an angle of 4.4 radians?
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Solution

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Solution Steps

To find the length of an arc in a circle, you can use the formula \( s = r \times \theta \), where \( s \) is the arc length, \( r \) is the radius of the circle, and \( \theta \) is the angle in radians. Given the radius and the angle, you can directly apply this formula to find the arc length.

Step 1: Given Values

We are given the radius \( r = 120 \, \text{km} \) and the angle \( \theta = 4.4 \, \text{radians} \).

Step 2: Arc Length Formula

The formula for the arc length \( s \) is given by: \[ s = r \times \theta \]

Step 3: Calculate Arc Length

Substituting the given values into the formula: \[ s = 120 \, \text{km} \times 4.4 \, \text{radians} = 528.0 \, \text{km} \]

Step 4: Round the Result

Rounding \( 528.0 \) to the nearest tenth gives: \[ s \approx 528.0 \, \text{km} \]

Final Answer

\(\boxed{s = 528.0 \, \text{km}}\)

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