N circle o, radius oq measures 9 inches and arc pq measures 6π inches. what is the measure, in radians, of central angle poq? 2pi/3 radians 3pi/4 centimeters 4pi/3 radians 3pi/2…

Question

asked Dec 23, 2018 111k views

2 Answers

Marzi Heidari · Answer 1 · 2018-12-29T04:19:35+0000

Answer:
$(2\pi)/(3)$ radians

Explanation:

Given: In circle O, the radius of circle = 9 inches

The arc length of PQ=
$6\pi$ inches

Let
$\theta$ be the measure of the angle .

The formula to calculate arc length(l) for radius r and angle x is given by :-

$l=r*\x\\\\\Rightarrow\ x=(l)/(r)$

According to the question we have,

$\theta=(6\pi)/(9)=(2\pi)/(3)$

Hence, the measure, of central angle POQ=
$(2\pi)/(3)$ radians