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Hello.
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What will help us solve this problem is what we know about the area of a circle, which is pi r squared.
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The area of a sector then, which is just part of a circle, is pi r squared times the central angle over 360.
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And lastly, what will help us is what we know about a special right triangle, a 3060 90 triangle.
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If the shortest leg, the shortest side is a, by hypotenuse is twice that distance.
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In the medium size, side or the bigger of the two legs is the square of three times a.
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So let's put all these ideas together to solve this problem and find the shaded area.
00:48
Since we're given that ta is 12 radical 3 and we're told that that's 30 degrees and this is tangent, that means the remaining angle at the center is 60 degrees.
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And this looks very similar to our 30 60 90 prototype that we drew.
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That means that 12 root 3 is equal to radical 3 times some number a, that means a itself, the shortest side is 12, which is the radius of the circle...