Question

How many triangles have three angles that are all perfect squares when measured in degrees

Answer 1

Answer:

there are three triangles you have

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Answer 2

HEY MATE!, HERE IS YOUR ANSWER

Answer:

102,82,42

Step-by-step explanation:

one triangle, with angles 100∘,64∘,16∘

We want to find angles x∘, y∘ and z∘ so that

x2+y2+z2=180.

We know that the largest angle must be smaller than 180∘ and bigger than 180∘/3=60∘. So the largest angle must be 169∘,144∘,121∘,100∘,81∘ or 64∘.

largest angle medium angle smallest angle all squares?

169 9 2 no

4 7 no

144 36 0 not a triangle

25 11 no

16 20 no

121 49 10 no

36 23 no

100 64 16 yes!

49 31 no

36 44 no

81 81 18 no

64 35 no

49 50 no

64 64 52 no

49 67 no

So there is exactly one triangle with all three angles perfect squares, viz a triangle with angles 102,82,42

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