Question

Using the converse of the Pythagorean Theorem and the following triangle leg lengths, classify the triangle: 2", 3", 4" ... is it right, acute, or obtuse?

Answer 1

If it is a right triangle then the longest side is equal to the square root of the sum of the other two sides squared. If c is the longest side, and the other two sides are a, and b, then :
\[c=\sqrt{a ^{^{2}}+b ^{2}}\]

Answer 2

Make the test.

Answer 3

That equals like 3.6 though, right?

Answer 4

2^2 + 3^2 < 4^2
so triangle is obtuse

also using law of cosines
2^2 + 3^2 -2*2*3cosx = 4^2
cosx = -1/4
x=104 degrees

Answer 5

a squared = 4
b squared = 9

The saquare root of 13 = 3.6 that is not a right triangle

Answer 6

Clarifying dumbcow use of the laws of cosines, it would be better to express the equation as:
\[(2^{2}+3^{2}-4^{2})/(2\times a \times b)=\cos -.25\]
\[\cos^{-1} -.25=104 ^{o}\]