Question

question 5 of 10
a dog that has been tethered with a ____foot lead makes the path shown here. the length of the path is 45 feet, and the measure of the angle θ is 2.25 radians.
image of a circle with a central angle of 2.25 radians and an arc length of 45 ft
answer here
blank line with a division symbol button

Explanation:

Step1: Recall the arc length formula

The formula for the length of an arc \( s \) in radians is \( s = r\theta \), where \( r \) is the radius (length of the lead) and \( \theta \) is the central angle in radians.

Step2: Solve for \( r \)

We know \( s = 45 \) feet and \( \theta = 2.25 \) radians. Rearranging the formula \( s = r\theta \) to solve for \( r \), we get \( r=\frac{s}{\theta} \).
Substituting the given values: \( r = \frac{45}{2.25} \)

Step3: Calculate the value

\( \frac{45}{2.25}=20 \)

Answer:

20