Question

the radius of a circle is 1 mile. what is the length of a 135° arc?
135°
r=1 mi
give the exact answer in simplest form.
miles

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute given values

Here, $\theta = 135^\circ$ and $r = 1$ mile. Substituting these into the formula: $L = \frac{135^\circ}{360^\circ} \times 2\pi \times 1$.

Step3: Simplify the expression

First, simplify $\frac{135}{360}$. We can divide numerator and denominator by 45: $\frac{135\div45}{360\div45}=\frac{3}{8}$. Then, the expression becomes $\frac{3}{8} \times 2\pi$. Simplify $\frac{3}{8} \times 2\pi$: $2$ and $8$ can be simplified (divide numerator and denominator by 2), so we get $\frac{3}{4}\pi$.

Answer:

$\frac{3}{4}\pi$