Question

Determine the angle at the centre of a circle with a radius of 8.0 cm for an arc length of 12.0 cm.

A. 2/3 radians
B. 1/3 radians
C. 3/2 radians
D. 3π / 2 radians

Answer 1

C. 3/2 Radians

Explanation:

As we know, a radian is defined as "the angle enclosed by an arc equal to the radius", or some variant of such.

This means 1 radian in this circle would have an arc length of 8cm.

Simple proportions should get you an answer:

`(1 \: radians)/(8cm) = (x \: radians)/(12cm) \\ 8x = 12 \\ x = (12)/(8) \\ x = (3)/(2)`