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What is the measure of central angle, θ, in degrees?Use 3.14 for π. Round your answer to the nearest whole number.

What is the measure of central angle, θ, in degrees?Use 3.14 for π. Round your answer-example-1

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We are asked to determine the angle of the given sector of a circle. To do that we will use the following relationship:


S=r\theta

Where:


\begin{gathered} S=\text{ arclength} \\ r=\text{ radius} \\ \theta=\text{ angle} \end{gathered}

Now, we solve for the angle by dividing both sides by "r":


(S)/(r)=\theta

Now, we substitute the values:


(8.75ft)/(6.2ft)=\theta

Solving the operations:


1.41rad=\theta

This angle is in radians. To convert to degrees we will use the following conversion factor:


\pi\text{rad}=180\text{degrees}

Now, we multiply by the conversion factor:


1.41\text{rad}*(180degrees)/(\pi rad)

We will use 3.14 for pi:


1.41\text{rad}*(180degrees)/(3.14rad)

Solving the operations:


1.41\text{rad}*(180degrees)/(3.14rad)=80.82

Therefore, the angle is approximately 81 degrees.

User Vineeth Venugopal
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