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 f…

Question

asked Jul 21, 2023 112k views

1 Answer

Frouo · Answer 1 · 2023-07-27T01:02:30+0000

Answer:

The length of the arc AC is;

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;