Questions: Find the radian measure of the central angle of a circle of radius 2 yards that intercepts an arc of length 3 yards. The radian measure of the central angle is (Type an integer or a fraction. Simplify your answer.)

Solution Steps

To find the radian measure of the central angle, we can use the formula for the arc length of a circle, which is given by \( \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \). We can rearrange this formula to solve for the central angle: \( \text{Central Angle} = \frac{\text{Arc Length}}{\text{Radius}} \).

We are given the arc length of a circle as \(3\) yards and the radius of the circle as \(2\) yards.

The formula to find the central angle \(\theta\) in radians is: \[ \theta = \frac{\text{Arc Length}}{\text{Radius}} \]

Substitute the given values into the formula: \[ \theta = \frac{3}{2} = 1.5 \]

Final Answer