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, q?
o θ = 5/7
o θ = 7/5
o θ = 7 + 5
o θ = 7 5

Explanation:

Step1: Recall 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 know \( s = 7 \) ft and \( r = 5 \) ft. From \( s = r\theta \), we can solve for \( \theta \) by dividing both sides of the equation by \( r \). So, \( \theta=\frac{s}{r} \).
Substituting \( s = 7 \) and \( r = 5 \) into the formula, we get \( \theta=\frac{7}{5} \).

Answer:

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