Question

Circle O shown below has a radius of 4 inches. Find, to the nearest tenth, the radianmeasure of the angle, x, that forms an arc whose length is 6 inches.X4 inches6 inches

Answer 1

We are asked to determine the angle "x" that will produce arclength of 6 inches in a circle with a radius of 4 inches. To do that we will use the following formula:

`S=r\theta`

Where:

`\begin{gathered} S=\text{ arclength} \\ r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}`

Now, we solve for the angle by dividing both sides by "r":

`(S)/(r)=\theta`

Now, we plug in the values:

`(6in)/(4in)=\theta`

Now, we solve the operations:

`1.5rad=\theta`

Therefore, the angle is 1.5 radians.