Given a circle with radius of 2, which is the degree measure of an arc whose length is 1/2 pie ?

Question

asked Sep 9, 2019 71.0k views

2 Answers

Kikocorreoso · Answer 1 · 2019-09-14T14:15:30+0000

Formula to find the arc length is:

$s=(\theta)/(360) 2\pi r$

So, if we want to measure the central angle then it will be:

$\theta= (360s)/(2r\pi)$

Where, s= arc length,

r = radius of the circle

$\theta$ = central angle in degrees.

According to the given problem,
$s=(1)/(2) \pi$ and r = 2.

So, first step is to plug in these values in the above formula.

$\theta=(360*(1)/(2)\pi)/(2*2\pi)$

=(360*(1)/(2))/(2*2)

π has been cancel out from both top and bottom.

=(180)/(4)

=45

So, measure of central angle is 45°.