1 Answer

Jonchang · Answer 1 · 2023-05-23T22:56:37+0000

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.

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