Questions: In a circle of radius 5 miles, the length of the arc that subtends a central angle of 3 radians is □ miles.

In a circle of radius 5 miles, the length of the arc that subtends a central angle of 3 radians is □ miles.
Transcript text: In a circle of radius 5 miles, the length of the arc that subtends a central angle of 3 radians is $\square$ miles. Question Help: Worked Example 1
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given a circle with radius \(r = 5\) and a central angle \( heta = 3\) radians. We need to find the length of the arc that this angle subtends.

Step 2: Apply the Formula

The length of the arc \(L\) can be found using the formula \(L = r \times \theta\).

Step 3: Substitute the Values and Calculate

Substituting the given values, we get \(L = 5 \times 3 = 15\).

Step 4: Round the Result

Rounding the result to 2 decimal places, we get \(L = 15\).

Final Answer:

The length of the arc is approximately 15 units.

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