I could look it up but the proof is trivial. Vector representing side c is vector of side a + vector of side b. Therefore, their dot products are equal, and when you expand that it's c = sqrt(a^2 + b^2 - 2abcos(angle))
You’re a hoot! All that sophisticated dithering and equational BS and you *still* don’t have an answer (because you’ve decided you don’t know the angle).
Dude! It’s a JOKE! And clearly a 3-4-5 right triangle. :-)
Hold a sheet of paper up to it if you’re not sure. That’s what Thomas Edison would do.
I’m glad I’m not paying you to do anything for me. I’d go broke.
Are you a lawyer? Or a politician?
Also, note that 24 does not work for the extreme cases. When angle = 90, the resultant is 5 (Pythagoras.) But when the angle is 0, the answer must be 4-3=1 (it is, sqrt(25-24).) Finally, when the angle is 180, the length of the side must be 4+3=7. The only way you can get there is sqrt(25-24cos(180)) = sqrt(25+24) = sqrt(49) = 7.
Yeah I brain farted.