Question

A circle has a central angle measuring 3pi/4 radians that intersects an arc of length 45 in. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for pi

Answer 1

Answer: The radius of the circle is 19.1 inches.

The length l of an arc corresponding to a central angle x (in radians) is:

$l = x\cdot r$

Given the values for l and x:

$45 = \frac{3}{4}\pi\cdot r\\\implies r = \frac{4}{3\pi}45=\frac{60}{\pi}\approx\frac{60}{3.14}\approx 19.1$

The above is in inches.