The pendulum on a clock swings through an angle of 1 radian, and the tip sweeps out ann arc of 12 inches. How long is the pendulum?

Options

A. 3.8 inches
B. 6 inches
C. 7.6 inches
D. 12 inches

Explanation

To find the length of the pendulum, we can use the relationship between the angle in radians, the arc length, and the radius (which in this case is the length of the pendulum). The formula we will use is:

\[ \text{Angle (in radians)} = \frac{\text{Arc Length}}{\text{Radius}} \]

Given:
- The angle \( \theta = 1 \) radian
- The arc length \( s = 12 \) inches

We need to find the radius (length of the pendulum), denoted as \( L \).

### Step-by-Step Solution:

1. **Write the formula**:
\[ \theta = \frac{s}{L} \]

2. **Substitute the known values into the formula**:
\[ 1 = \frac{12}{L} \]

3. **Rearrange the equation to solve for \( L \)**:
\[ L = \frac{12}{1} \]

4. **Calculate \( L \)**:
\[ L = 12 \text{ inches} \]

Thus, the length of the pendulum is \( 12 \) inches.