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

Answer:

$\theta=\dfrac{7}{4}\ \text{radian}$

Step-by-step 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 :

$l=r\times \theta$

$\theta$ is central angle

$\theta=\dfrac{l}{r}\\\\\theta=\dfrac{21}{12}\\\\\theta=\dfrac{7}{4}\ \text{radian}$

So, the angle at the centre of the circle is $\dfrac{7}{4}\ \text{radian}$.