Questions: In a circle of radius 7 miles, the length of the arc that subtends a central angle of 5 radians is miles.

Solution Steps

To find the length of the arc in a circle, we can use the formula for the arc length, which is given by $\text{Arc Length} = \theta \times r$, where $\theta$ is the central angle in radians and $r$ is the radius of the circle. Given the radius and the central angle, we can directly apply this formula.

We are given the radius of the circle $r = 7$ miles and the central angle $\theta = 5$ radians.

The formula for the length of an arc in a circle is: $$\text{Arc Length} = \theta \times r$$

Substitute $\theta = 5$ radians and $r = 7$ miles into the formula: $$\text{Arc Length} = 5 \times 7$$

Perform the multiplication: $$\text{Arc Length} = 35 \text{ miles}$$

Final Answer