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a circle has a radius of 5 ft and an arc of lentgh 7 ft is made by the intersection of the circle with a central angle which equation gives the measure of the central angle, q
0÷5/7
0=7/5
0=7+5
0=7×5​

Verified Answer :

semsee45

Answer:

\(\textsf{B)}\quad \theta=\dfrac{7}{5}\)

Step-by-step explanation:

To find the equation that gives the measure of the central angle q, we can use the arc length formula:

\(\boxed{\begin{array}{l}\underline{\textsf{Arc length}}\\\\s=r \theta\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{$s$ is the arc length.}\\ \phantom{ww}\bullet\; \textsf{$r$ is the radius.}\\ \phantom{ww}\bullet\;\textsf{$\theta$ is the angle measured in radians.}\end{array}}\)

In this case:

  • s = 7 ft
  • r = 5 ft
  • θ = central angle q

Substitute the values into the formula and solve for θ:

\(7=5 \cdot \theta\\\\\\\theta=\dfrac{7}{5}\)

Therefore, the equation that gives the measure of the central angle is:

\(\Large\boxed{\boxed{\theta=\dfrac{7}{5}}}\)

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