Question

What is the arc length of arc CD in the circle below? Circle A is shown with a radius labeled 15 feet and a central angle marked 45 degrees.

Answer 1

It would be 11.78 or 11.8 rounded

Answer 2

The circumference of a circle is found using the formula:


`C=2 \pi R`,

where R is the radius of the circle. So the circumference of our circle is


`C=2 \pi R\approx 2\cdot15\cdot 3.14=94.2` (ft).


The ratio of the arc length to the circumference is equal to the measure of the central angle to the complete angle. That is:


`\displaystyle{ (45^(\circ))/(360^(\circ)) = (a.length)/(94.2)`.


`\displaystyle{ (1)/(8)= (a.length)/(94.2) \rightarrow a.length= (94.2)/(8)= 11.775(ft)`.


Answer: 11.8 (ft)