Question

Consider circle c with angle 3/4 radians. If minor arc AB measures 9n inches, what is the length of

the radius of circle C? If necessary, round your answer to
the nearest inch.
6 inches
12 inches
18 inches
24 inches

Answer 1

B.) 12 inches

Explanation:

Answer 2

The radius of circle is 12 inches

Solution:

Given that,

Consider circle c with angle
`(3 \pi )/(4) \text{ radians }`

Minor arc AB measures
`9 \pi` inches

Therefore, we can say,

`Central\ angle\ in\ radians = (3 \pi )/(4)\\\\Arc\ length = 9 \pi`

To find: Radius of circle

The length of arc when angle given in radians is:

`s = r * \theta`

Where,

"s" is the arc length and "r" is the radius and
`\theta` is the central angle in radians

`9 \pi = r * (3 \pi )/(4)\\\\r = 9 * (4)/(3)\\\\r = 12`

Thus the radius of circle is 12 inches