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: $\theta\approx1.78\ rad$

Step-by-step 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:

$\frac{s}{r}=\frac{r\theta}{r}\\\\\theta=\frac{s}{r}$

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:

$\theta=\frac{21.3\ in}{12\ in}$

Finally, evaluating, you get the following result:

$\theta=1.775\ rad$

Rounded to the nearest hundredth of a radian:

$\theta\approx1.78\ rad$