Questions: In a circle of radius 7 miles, the length of the arc that subtends a central angle of 5 radians is miles.

In a circle of radius 7 miles, the length of the arc that subtends a central angle of 5 radians is miles.
Transcript text: In a circle of radius 7 miles, the length of the arc that subtends a central angle of 5 radians is $\square$ miles.
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Solution

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Solution Steps

To find the length of the arc in a circle, we can use the formula for the arc length, which is given by \( \text{Arc Length} = \theta \times r \), where \( \theta \) is the central angle in radians and \( r \) is the radius of the circle. Given the radius and the central angle, we can directly apply this formula.

Step 1: Identify the Given Values

We are given the radius of the circle \( r = 7 \) miles and the central angle \( \theta = 5 \) radians.

Step 2: Use the Arc Length Formula

The formula for the length of an arc in a circle is: \[ \text{Arc Length} = \theta \times r \]

Step 3: Substitute the Given Values

Substitute \( \theta = 5 \) radians and \( r = 7 \) miles into the formula: \[ \text{Arc Length} = 5 \times 7 \]

Step 4: Calculate the Arc Length

Perform the multiplication: \[ \text{Arc Length} = 35 \text{ miles} \]

Final Answer

\(\boxed{35 \text{ miles}}\)

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