An arc 15 ft long describes an angle of 5 radians at the centre of a circle. Find the radius of the circle.

Answer

To find the radius of the circle given that an arc of length 15 ft describes an angle of 5 radians at the center, we can use the formula for the length of an arc:

\[ L = r \cdot \theta \]

where:
- \(L\) is the length of the arc,
- \(r\) is the radius of the circle,
- \(\theta\) is the angle in radians.

### Step 1: Write down the formula for the length of an arc.
The formula is:
\[ L = r \cdot \theta \]

### Step 2: Substitute the known values into the formula.
We know:
- \(L = 15\) ft (length of the arc),
- \(\theta = 5\) radians.

Substituting these values into the formula gives:
\[ 15 = r \cdot 5 \]

### Step 3: Solve for the radius \(r\).
To isolate \(r\), divide both sides of the equation by 5:
\[ r = \frac{15}{5} \]

### Step 4: Calculate the value of \(r\).
\[ r = 3 \text{ ft} \]

### Conclusion:
The radius of the circle is \(3\) feet.

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