## anonymous 5 years ago 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?

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 : $c=\sqrt{a ^{^{2}}+b ^{2}}$

Make the test.

3. anonymous

That equals like 3.6 though, right?

4. anonymous

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

a squared = 4 b squared = 9 The saquare root of 13 = 3.6 that is not a right triangle

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