The radius of a circle is 5 inches. What is the angle measure of an arc a inches long?

Question

asked Aug 12, 2021 4.3k views

2 Answers

Daniel Bastidas · Answer 1 · 2021-08-19T01:10:51+0000

The radius of a circle is 5 inches so, the angle measure of the arc is
$(\pi)/(5)$ radians or 36 degrees.

The formula to find the angle measure (in radians) of an arc in a circle is given by:

$\theta=(\ell)/(r)$

where:

θ is the angle measure in radians,

ℓ is the length of the arc,

r is the radius of the circle.

In this case, you have
$\ell=\pi \text { inches}$ and
$r=5 \text { inches}$ . Plugging in these values into the formula:

$\theta=(\pi)/(5)$

So, the angle measure of the arc is
$(\pi)/(5)$ radians.