Question

no additional details were added for this assignment. fill in the blanks to complete the sentences. use the keypad to enter your answers in the boxes. an arc with a length equal to the radius of a circle subtends a central angle measuring rad. as such, for any arc length s and radius r, the radian measure of the central angle subtended by the arc is given by: $\theta=\frac{s}{r}$ rad. if the arc length is 5 units and the radius is 2 units, $\theta =$ rad.

Explanation:

Step1: Recall radian - definition

By definition, when the arc - length $s$ is equal to the radius $r$ of a circle, the radian measure of the central angle $\theta$ is given by the formula $\theta=\frac{s}{r}$. Substituting $s = r$ into the formula, we get $\theta=\frac{r}{r}=1$ rad.

Step2: Calculate the central - angle for given $s$ and $r$

We are given that $s = 5$ units and $r = 2$ units. Using the formula $\theta=\frac{s}{r}$, we substitute the values of $s$ and $r$ into it. So, $\theta=\frac{5}{2}=2.5$ rad.

Answer:

1
2.5