Question

a circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. which equation gives the measure of the central angle, θ?
○ $\theta = \frac{5}{7}$
○ $\theta = \frac{7}{5}$
○ $\theta = 7 + 5$
○ $\theta = 7 \cdot 5$

Explanation:

Step1: Recall the arc length formula

The formula for the length of an arc \( s \) in a circle with radius \( r \) and central angle \( \theta \) (in radians) is \( s = r\theta \).

Step2: Solve for \( \theta \)

We need to find \( \theta \), so we rearrange the formula \( s = r\theta \) to solve for \( \theta \). Dividing both sides of the equation by \( r \), we get \( \theta=\frac{s}{r} \).

Step3: Substitute the given values

We know that the arc length \( s = 7 \) ft and the radius \( r = 5 \) ft. Substituting these values into the formula \( \theta=\frac{s}{r} \), we have \( \theta = \frac{7}{5} \).

Answer:

\(\boldsymbol{\theta=\frac{7}{5}}\) (corresponding to the option \( \theta=\frac{7}{5} \))