SOLUTION: The measures of the angles of a triangle are in the extended ratio 2:2:8. What is the measure of the smallest angle?
Is this even possible? The perimeter of the triangle is not
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Question 513821: The measures of the angles of a triangle are in the extended ratio 2:2:8. What is the measure of the smallest angle?
Is this even possible? The perimeter of the triangle is not given?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Of course it is possible, and the perimeter is immaterial. The perimeter could be 3 nanometers or 17 light-years -- we don't care.
Recall that the sum of the interior angles of any triangle is 
. So, let 
be an arbitrary constant of proportionality and given that the ratio of the angles is given as 2:2:8, we can say:
Solve for and then calculate 
and 
to get the measure of the three angles. Technically, there is no "the smallest" angle since this turns out to be an isosceles triangle with the largest angle at the apex. However, the value of should suffice to answer your question.
John
My calculator said it, I believe it, that settles it
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