Question

If the arc length shown in blue is 21.3 inches, then 0 to the nearest hundredth of a
radian is

Answer 1

Answer:
`\theta\approx1.78\ rad`

Explanation:

By definition, the Arc lenght can be calculated with the following formula:

`s=r\theta`

Where "s" is the Arc lenght, "r" is the radius and
`\theta` is the central angle measured in radians.

From that equation you can solve for
`\theta` dividing both sides of the equation by the radius "r", then:

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

According to the information given in the exercise:

`s=21.3\ in`

And you can identify in the figure that the radius of the circle is:

`r=12\ in`

Therefore, you can substitute values into the equation:

`\theta=(21.3\ in)/(12\ in)`

Finally, evaluating, you get the following result:

`\theta=1.775\ rad`

Rounded to the nearest hundredth of a radian:

`\theta\approx1.78\ rad`