Question

find the arc length of $overset{\frown}{ab}$. round your answer to the nearest hundredth.
8 ft
$45^{\circ}$

Explanation:

Step1: Recall arc length formula

The formula for arc length is $s = 2\pi r \times \frac{\theta}{360^\circ}$, where $r$ is the radius, and $\theta$ is the central angle in degrees.

Step2: Identify given values

Here, $r = 8$ ft, $\theta = 45^\circ$. Substitute into the formula:
$s = 2\pi \times 8 \times \frac{45^\circ}{360^\circ}$

Step3: Simplify the expression

First simplify $\frac{45}{360} = \frac{1}{8}$, then calculate:
$s = 16\pi \times \frac{1}{8} = 2\pi$

Step4: Compute decimal value

Calculate $2\pi \approx 2 \times 3.1416 = 6.2832$, then round to the nearest hundredth.

Answer:

6.28 ft