Added by Hung Doan on January 29, 1999 at 23:02:39:
Given: two sides and INCLUDED angle, find third sideó works with any triangle:
A triangle with sides a,b,c and angles opposite sides A, B, C (the upper caps are angles)
If you notice, this Pythagorean "extended", cosine of 90 degrees is 0, therefore, if you have a right triangle, this works out, and now with ANY triangle. Cool huh?
Dear Fellow Students, I goofed on my first "Law of Cosines" entry, the following is updated:
Given ANY triangle and the Side-Angle-Side situation, one can find the length of the third side. Ok, given three sides a, b, c, and opposite angles A, B, C (A is opposite side a, for example) the following is true:
c^2 = a^2 + b^2 -2ab cosineC, and of course, if the included angle is 90 degrees, then the "2abCosC" term goes away, because Cosine 90=0. There ya go.