Given the side lengths of 20,23 and 41, determine whether the triangle is acute, right, obtuse, or not a triangle.

 Obtuse triangle

Explanation:

In this case, a triangle is possible since adding any two sides leads to a sum larger than the third side

20+23 = 43 is larger than 4120+41 = 61 is larger than 2323+41 = 64 is larger than 20

I'm using the triangle inequality theorem here.

To determine what kind of triangle we have, we'll use the converse of the Pythagorean theorem. Specifically, we'll use a corollary of it.

Consider a triangle with sides a,b,c. Let c be the longest side.

We have three possible cases:

If a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 > c^2, then the triangle is acute.If a^2+b^2 < c^2, then the triangle is obtuse.

For this problem, we have a = 20, b = 23, c = 41.

We see that a^2+b^2 = 20^2+23^2 = 929 and c^2 = 41^2 = 1681.

In short, a^2+b^2 = 929 and c^2 = 1681.

Since 929 < 1681, this means a^2+b^2 < c^2.

Therefore, this triangle is obtuse.

Your answer should be 1/3. i hope i could ! good luck : )

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