Question

Determine the angle at the centre of a circle with radius 12.0 cm for an arc length of of 21.0 cm.

A. 4/7 radians
B. 7/π radians
C. 7/4 radians
D. 7 π/4 radians

Answer 1

`\theta=(7)/(4)\ \text{radian}`

Explanation:

We have,

Radius of the circle is 12 cm

Arc length, l = 21 cm

It is required to find the central angle of the circle. The formula for the length of an arc of a circle is :

`l=r* \theta`

`\theta` is central angle

`\theta=(l)/(r)\\\\\theta=(21)/(12)\\\\\theta=(7)/(4)\ \text{radian}`

So, the angle at the centre of the circle is
`(7)/(4)\ \text{radian}`.