SOLUTION: One angle of a triangle is 1/3 the largest angle, but twice the smallest. Find the largest angle.

Question 205783: One angle of a triangle is 1/3 the largest angle, but twice the smallest. Find the largest angle.
Answer by Targetweek(62) (Show Source): You can put this solution on YOUR website!
First we will start out assigning variables
x = shortest side
y = middle side
z = longest side
1.Because all the interior angles of a triangle have to add up to 180 be can write the following equation
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2. Next we write tow additional equations dealing with each variable independantly
3. Because we want to solve for the longest side, z , then we need to write two equations, one where x is by itself (in fancy terms, x in terms of z), and the other where y is by itself (y in terms of z)
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a. Becuase the problem doesn't describe z in terms of x we will have to make one by substituting
b. because we can substitue that value into this equation
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c. Now solve for x
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d. Now we have the two equations
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3. Now substitute those equations back into the first equation
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4. Finally solve for z
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5. So the largest angle is 120 degrees
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