Question 1186011: In a triangle the measure of the greatest angle is square of the measure of the smallest angle., and the other angle is double of the smallest angle. Find the measure of the greatest angle. (Applying Quadratic equations)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let a = the smallest angle
let b = the middle angle
let c = the largest angle.
in a triangle, the sum of all the angles is 180 degrees.
therefore:
a + b + c = 180
c = a^2 and b = 2a.
the formula becomes:
a + 2a + a^2 = 180
combine like terms to get:
3a + a^2 = 180
subtract 180 from both sides of the equation and order the terms in descending order of degree to get:
a^2 + 3a - 180 = 0
factor this quadratic equation to get:
(a + 15) * (a - 12) = 0
solve for a to get:
a = -15 or a = 12
since a has to be positive, then a = 12.
a^2 + 3a - 180 = 0 becomes 12^2 + 3*12 - 180 = 0 which becomes 144 + 36 - 180 = 0 which becomes 180 - 180 = 0 which becomes 0 = 0, confirming the value of 12 for a is good.
the sum of the angles was a^2 + 2a + a which is equal to 180.
this becomes 144 + 24 + 12 = 180 which becomes 180 = 180 which confirms the sum of the angles = 180 is true.
the biggest angle is 144 degrees and is equal to 12 squared.
the middle angle is 24 and is equal to 2 * 12.
the smallest angle is 12.
your solution is that the biggest angle is 144 degrees.
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