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.)

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

Transcript text: 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 $\square$ (Type an integer or a fraction. Simplify your answer.)

Solution

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}} $.

Step 1: Identify the Given Values

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

Step 2: Use the Formula for Central Angle

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

Step 3: Substitute the Given Values

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