SOLUTION: 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 greate

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.

RELATED QUESTIONS
the measure of one angle of a triangle is three times the measure of the smallest angle,... (answered by cleomenius)

the measure of the largest angle of a triangle is twice the measure of the smallest... (answered by greenestamps)

The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other (answered by rfer)

In a triangle the measure of the largest angle is 3 times the measure of the smallest... (answered by texttutoring)

in a certain right triangle, the measure of one angle is twice the measure of the... (answered by rfer)

The measure of one angle of a triangle is three times the measure of the smallest angle,... (answered by stanbon)

The measure of one acute angle of a right triangle is 12 degrees more than the other... (answered by Theo)

The measure of one angle of a triangle is 28 more than the measure of the smallest angle... (answered by rfer)

The sum of the measures of a triangle is 180°. The largest angle is twice the smallest... (answered by greenestamps)