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Geometry

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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?

Aug 29, 2021

#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?

An arithmetic progression means you get them by addition.  So,

Let the 1st angle be called (13)

Let the 2nd angle be called (13 + D)    D for difference

Let the 3rd  angle be called (13 + D + D)

We know that the sum of all three angles of a triangle is 180

(13) + (13 + D) + (13 + D + D)  =  180

39 + 3D  =  180

3D  =  180 – 39  =  141

D  =  141 / 3  =  47

Thus

The 1st angle  =  13

The 2nd angle  =  (13 + 47)  =  60

The 3rd angle  =  (13 + 47 + 47)  =  107 degrees

Check:  13 + 60 + 107 = 180

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Aug 29, 2021
#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?

It's me again.  I just re-read the question.  I overlooked that it says right triangle.  Disregard answer #1.

So one angle of a right triangle is 90 degrees.

Since the other two angles have to total the other 90 degrees, each of them is less than 90 degrees.

Therefore the largest angle is 90 degrees.

BTW, it's not necessary to determine the arithmetic progression, if there is one.

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Aug 29, 2021