Question

if the arc length shown in blue is 32.5 inches, then theta to the nearest hundredth of radian is ___.

Answer 1

well, if the arc is 32.5 units, and the radius of the circle, and thus of the angle is 12, as you can see in the picture, then


`\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ s=32.5\\ r=12 \end{cases}\implies 32.5=12\theta \implies \cfrac{32.5}{12}=\theta`

and surely you know how much that is.

Answer 2

∅ = 2.71

Explanation:

In the figure shown length of the arc = 32.5 and radius of the circle formed = 12.

∅ is the angle formed by arc of 32.5

We know arc = r.∅

Or ∅ = arc/r = 32.5/12 = 2.71

Answer is ∅ in radian is 2.71