Please help. Geometry.
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The area of the entire sector is
The area of the triangle OAB is .
So, the area of the segment is
Sum of all angles of a triangle is equal to 180°. Therefore,
A + B + C = 180
Given that, A = 4x, B = 3x + 1, C = 7x + 11.
Hence, we can set up an equation as following:
4x + 3x + 1 + 7x + 11 = 180
14x + 12 = 180 Combine the like terms.
14x + 12 -12 = 180 - 12 Subtract 12 from each sides.
14x = 168
Divide each sides by 14.
So, x= 12.
Now by plug in x=12 in the given expressions of A, B and C we can get the measure of eah angles of the triangle. Therefore,
A = 4x = 4(12) = 48
B= 3x + 1= 3(12) + 1 = 36 + 1 = 37
C= 7x + 11 = 7(12) + 11 = 84 + 11 =95
From the above result we can see that C is the largest angle and B is the smallest angle.
There is a relationship of a triangle which state that the largest side is opposite side of the largest angle and similarly smallest side is opposite side of the smallest angle.
Here AB is the opposite side of the largest angle C. So, AB is the largest side.
Similarly AC is the smallest side.
So, the order from shortest to longest is B: AC, BC, AB