answer: 39.3 feet
explanation:
- because you need to find the length of an arc, you should think about circumference. the formula for that is 2πr, where r is the length of the circle's radius.
- you don't need the whole circumference, though, so you'll need a fraction (in this case, it's 225/360, because 225° is the measure of the arc's angle and 360° is the measure of a full circle's rotation)
- multiply the circumference by this fraction to get the length of the arc.
work:
[tex]r = 10 ft\\C (circumference) = 2\pi r = 2\pi (10) = 20\pi \\\\20\pi * 225/360\\20\pi * 15/24\\= \frac{300\pi}{24} = 12.5\pi \\[/tex]
enter 12.5π into a calculator and it's about 39.3 after being rounded to the nearest tenth.
