A central angle of a circle of radius 50 cm intercepts an arc of 10 cm. Express the central angle `theta` in radians and in degrees.

Answer

To solve the problem step by step, we will find the central angle \( \theta \) in both radians and degrees.

### Step 1: Identify the given values
- Radius of the circle \( R = 50 \) cm
- Length of the arc \( L = 10 \) cm

### Step 2: Use the formula to find the central angle in radians
The formula to find the central angle \( \theta \) in radians is given by:
\[ \theta = \frac{L}{R} \]
Substituting the values:
\[ \theta = \frac{10 \text{ cm}}{50 \text{ cm}} = \frac{1}{5} \text{ radians} \]

### Step 3: Convert the angle from radians to degrees
To convert radians to degrees, we use the conversion factor:
\[ \text{Degrees} = \theta \times \frac{180}{\pi} \]
Substituting the value of \( \theta \):
\[ \text{Degrees} = \frac{1}{5} \times \frac{180}{\pi} \]
Calculating this:
\[ \text{Degrees} = \frac{180}{5\pi} = \frac{36}{\pi} \approx \frac{36}{3.14} \approx 11.46 \text{ degrees} \]

### Final Answers
- The central angle \( \theta \) in radians is \( \frac{1}{5} \) radians.
- The central angle \( \theta \) in degrees is approximately \( 11.46 \) degrees.