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 ten…

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asked Jan 8, 2019 177k views

1 Answer

Lakindu · Answer 1 · 2019-01-14T14:10:02+0000

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:

$45 = (3)/(4)\pi\cdot r\\\implies r = (4)/(3\pi)45=(60)/(\pi)\approx(60)/(3.14)\approx 19.1$

The above is in inches.