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A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet. What is the length of arc AC, in feet?

A sprinkler system is set up to water the sector shown in the accompanying diagram-example-1
User Danieleee
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1 Answer

6 votes

Answer:

The length of the arc AC is;


AC=20ft

Step-by-step explanation:

Given the radius AB as 20ft.


AB=20\text{ ft}

And angle ABC measures 1 radian.

Using the Method 1;

Length of Arc AC is;


AC=\omega r

Substituting the angle in radian and the radius;


\begin{gathered} AC=1*20\text{ ft} \\ AC=20\text{ ft} \end{gathered}

The length of Arc AC is 20 ft

Method 2;

We will firstly convert the angle from radian to degree.

As shown below;


\begin{gathered} \theta=1\text{ rad}*(180)/(\pi) \\ \theta=57.3^0 \end{gathered}

Then we will apply the formula for calculating the length of an arc;


C=(\theta)/(360)*2\pi r

Substituting the value of the angle and the radius.


\begin{gathered} C=(57.3)/(360)*2\pi*20ft \\ C=(57.3)/(360)*40\pi ft \\ C=20ft \end{gathered}

Therefore, the length of the arc AC is;


AC=20ft

User Frouo
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