Question

The radius of a circle is 3 inches. What is the measure, in radians, of the angle subtended by an arc 3π inches long

Answer 1

`\theta\text{ = }\pi\text{ radians}`

Step-by-step explanation

We are given that the radius of the circle is 3 inches and the length of the arc that subtends the angle is 3π inches.

We can find the angle subtended by the arc by using the formula for length of an arc:

`\begin{gathered} L\text{ = }(\theta)/(2\pi)\cdot\text{ 2}\pi R \\ \text{where }\theta\text{ = angle subtended, in radians} \\ R\text{ = radius} \end{gathered}`

Therefore, we have that:

`\begin{gathered} 3\pi\text{ = }(\theta)/(2\pi)\cdot\text{ 2}\cdot\pi\cdot3 \\ \Rightarrow3\pi\text{ = }\theta\cdot\text{ 3} \\ \text{Divide through by 3:} \\ \theta\text{ = }\pi\text{ radians} \end{gathered}`

That is the angle subtended by the arc.