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# help

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The angles in a right triangle form an arithmetic progression.  If the smallest angle is 13 degrees, then what is the largest angle?

Jul 2, 2020

#1
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The angles in a right triangle form an arithmetic progression.  If the smallest angle is 13 degrees, then what is the largest angle?

The total of the internal angles of every triangle is 180o

The right angle in the right triangle takes up 90o of those 180o

Thus, the largest angle in a right triangle always has to be the right angle, i.e. 90o

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Jul 2, 2020
#2
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The angles in a right triangle form an arithmetic progression.  If the smallest angle is 13 degrees, then what is the largest angle?

I think that nither arithmetic nor geometric progression can be applied to the angles of the right triangle.

arithmetic progression       13º         51.5º       90º       wrong!

geometric progression        13º            34.205275º            90º

Jul 3, 2020
#3
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The angles in a right triangle form an arithmetic progression.  If the smallest angle is 13 degrees, then what is the largest angle?

1.  IF you'd said the smallest angle is 30o instead of 13o

then we could have an arithmetic progression.

30o - 60o - 90o  the largest angle still is the 90o angle.

In a right triangle, the 90o angle is always the largest

angle because neither of the other angles can be 90o

2.  IF you'd said simply triangle, instead of right triangle,

then the arithmetic progression is 13o - 60o - 107o

Did you really mean to ask one of the two cases above?

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Jul 3, 2020