Question

If a circle has a radius of 10 cm how do you find the length of an arc subtended by a central angle measuring 1.5 radians?

Answer 1

`15cm`

Explanation:

Arc length is given by:

`A =rtheta`

Where A is arc length.

`:.`

`A=(10)(1.5)=15cm`

This makes sense, if you consider how we define a radian measurement.

If the radius of a unit circle (radius 1) describes an arc on the circumference equal to its length, then the angle subtended by this arc is defined as 1 radian.

So, if we have a radius of 10cm, and it describes an arc 1.5 times its length, then the length of the arc is 15cm.