To find the arc length of $AB$ in the given circle, we can follow these steps:

Step 1: Identify the Given Values

• Radius: $r = 8$ feet.
• Central Angle: $\theta = 45^\circ$.

Step 2: Use the Formula for Arc Length

The formula for the length of an arc is given by:

$\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r$

where:

• $\theta$ is the central angle in degrees.
• $r$ is the radius.
• $2\pi r$ is the circumference of the circle.

Step 3: Plug in the Values

$\text{Arc Length} = \frac{45}{360} \times 2\pi \times 8$

Step 4: Simplify the Expression

Let's calculate the value of the arc length:

$\text{Arc Length} = \frac{1}{8} \times 2\pi \times 8 = \pi \approx 3.14 \, \text{feet}$

Rounding to the nearest hundredth, the arc length of $AB$ is approximately 3.14 feet.

Let me know if you want a more detailed breakdown or have any questions!

Related Questions:

1. How do you find the arc length if the central angle is in radians?
2. What is the formula for the circumference of a circle?
3. How would the arc length change if the central angle is doubled?
4. What is the relationship between arc length and the radius?
5. How can you find the area of a sector using the central angle?

Tip:

When dealing with angles in degrees, always remember to convert them to radians if using the formula $\text{Arc Length} = \theta r$ (where $\theta$ is in radians).