Question

A circle has a radius of 17in . Find the radian measure of the central angle θ that intercepts an arc of length 16in . Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

There are \[2\pi\] radians per 360 degrees, or pi radians=180 degrees.
After having set this, you find the circumference of the circle: 17*2pi. You will have your circumference equal to 106.8141502220529701077298750315in. (The problem said not to round any intermediate computations, so you must keep all the numbers visible in your calculator.)
You now need to set up a ratio to find how many degrees there are per inch:
360degrees=106.8141502220529701077298750315inches, so divide both sides by your inches value to see how many degrees there are per inch.
3.3703399713577835809881267537868degrees=1 inch.
You want to find out how many radians there are in 16 inches of the circle. First you multiply both sides by 16:
53.925439541724537295810028060588 degrees=16 inches.
You then convert your degrees to radians: pi=180 degrees. You must set up the following:\[\frac{ rad }{ \pi }=\frac{ 53.925439541724537295810028060588 }{ 180 }\]
0.94radians=16inch arc (I decided to round to the nearest hundredth, but you may be counted off for not following all instructions, so you could simplify the answer to 0.9 radians)

Answer 2

appreciate it!