Posted by **eve** on Sunday, January 22, 2012 at 10:12am.

I need to find out the type of triangle (by the type of angles). Is triangle acute, right or obtuse, when the lenghts of triangle sides are:

a) 7, 8, 12

b) 20, 15, 40

c) 2/3, 8/9, 10/9

- math -
**Reiny**, Sunday, January 22, 2012 at 1:05pm
The largest angle is opposite the largest side.

So all we have to do is check if the largest side is greater or smaller than a "hypotenuse"

in 1st:

7^2 + 8^2 = 113

12^2 = 144

so 12^2 > 7^2 + 8^2

and the triangle is obtuse with the angle opposite 12 as > 90°

2nd:

a trick question!

To form a triangle, the sum of any two sides has to be greater than the third side,

but 20+15 is NOT greater than 40.

So we can't even form the triangle.

3rd:

2/3, 8/9, 10/9

or

6/9, 8/9, 10/9

this triangle has the same angles as

6 , 8, 9 (they are similar)

check for 9^2 vs 6^2 + 8^2

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