law of cosines?

Question

if an alternate form of law of cos is

CosA= b^2+c^2-a^2/ 2bc

can this be done?

CosB= a^2+c^2-b^2/ 2ac


will this work?

Answer 1

Yes as long as the Angle A in the first equation is between sides b and c and the Angle B in the second equation is between sides a and c.

Answer 2

I'm just trying to make sense of this. The way I learned it was
A SQR = B SQR + C SQR - 2 BC * Cos a

and I think the way you rewrote it was correct if my math is right, then just replacing B with A in the above model would give you,

B SQR = A SQR + C SQR - 2 AC * Cos b

or rewritten again you would come out to what you had, so yeah, your math appears to be all correct from my point of view, and I don't see any reason why it shouldn't, so would stick with that assumption until someone can prove you wrong, because everything looks absolutely correct.

So just to recap:

A SQR = B SQR + C SQR - 2 BC * Cos a , which equals,

Cos a = B SQR + C SQR - A SQR / 2 BC

And then substituting line A with B and vice-versa

B SQR = A SQR + C SQR - 2 AC * Cos b , which equals

Cos b = A SQR + C SQR - B SQR / 2 AC

Answer 3

The Law of Cosines states

a² = b² + c² - 2bc(cosA)

Solving for cosA we have
cosA = (-a² + b² + c²)/(2bc)
______________

b² = a² + c² - 2ac(cosB)

Solving for cosB we have
cosB = (a² - b² + c²)/(2ac)

So you are correct.

Answer 4

I'm not sure I just stick with

a(squared)=b(squared) x c (squared) +2(a)(b)(CosA)

Answer 5

Yeah, I'm pretty sure you can.