Questions: In a circle of radius 5 miles, the length of the arc that subtends a central angle of 1 radians is miles.

In a circle of radius 5 miles, the length of the arc that subtends a central angle of 1 radians is miles.
Transcript text: In a circle of radius 5 miles, the length of the arc that subtends a central angle of 1 radians is $\square$ miles.
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Solution

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Solution Steps

To find the length of an arc in a circle, we can use the formula: arc length = radius × central angle (in radians). Given the radius and the central angle, we can directly apply this formula to find the arc length.

Step 1: Identify the Given Values

We are given the radius of the circle \( r = 5 \) miles and the central angle \( \theta = 1 \) radian.

Step 2: Apply the Arc Length Formula

The formula for the length of an arc \( L \) is given by: \[ L = r \cdot \theta \] Substituting the known values: \[ L = 5 \cdot 1 \]

Step 3: Calculate the Arc Length

Calculating the above expression: \[ L = 5 \text{ miles} \]

Final Answer

The length of the arc that subtends a central angle of 1 radian is \\(\boxed{5}\\) miles.

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