Question

The radius of a circle is 4 miles. What is the length of a 45° arc?

45°
r=4 mi
Give the exact answer in simplest form.

Answer 1

2π miles

Explanation:

2πr is the formula for the circumference of a circle.

Using that formula, the circumference for this circle is 8π.

Since the circle's full angle is 360°, we can use a ratio to find out how long the 45° arc is.

° : length

360 : 8π

9 : 0.4π

45 : 2π

The 45° is 2π mi long.