Question

please explain STEP BY STEP....im also used to degrees so radians are absolutely new to me

Answer 1

Okay, so basically we are given that the central angle of the circle = \(\frac{\pi}{3}\)
Also, the area of the sector = 23 ft^2

Find the radius of the circle.

There are many ways to solve this. But to give you an insight into radians, I'll explain the radian method of solving this.

This is the diagram.


Getting it till here? :)

Answer 2

yea...i am @AkashdeepDeb at least i have understood that

Answer 3

Okay.

So now let us understand the area of the sector formula in degrees.

\[Area~of~a~circle = \pi r^2\]
\[Area~of~a~sector = \frac{\theta}{360} \pi r^2\]

Do you know why?
Because, sector is just a part of the circle, so that part of the circle depends on how much the central angle \(\theta\) is. So that is why when \(\theta\) is 360 degrees, it is just the full circle.
When \(\theta\) is 180 degrees it is half the circle.
When it is 90, it is a quadrant.

Getting this till here?

Answer 4

yes @AkashdeepDeb ...let me close this question though, but keep explaining

Answer 5

ugh...wait @rational @AkashdeepDeb

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How could you let me do this.

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Answer 23

Okay.

Let us understand the difference between degrees and radians.
Now, radians are very simple. They are just another form of measuring angles.
So, basically, they are just like degrees.

radians are defined as \(\frac{arc~length}{radius}\)

Here, check this out, it explains it extremely well: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/radians-and-degrees

Formula of area of sector where \(\theta\) is in radians = \(\frac{1}{2} r^2 \theta\)

Use that to get the radius. But do watch the video. It is very helpful. :)

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i came to ruin the post

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Damn right Squ. xD

Answer 36

Hell no, we won't go!