question about cosine law

Question

for the cosine law c^2= a^+b^2-2abcosc, is the value for c always the longest angle of the triangle, and if so, how do you know which side is the longest given only 2 sides and 1 angle?

Answer 1

No, c is not necessarily the longest side.

 

If the sides are called a, b, c, let  C = angle opposite side c, let B = angle opposite side b, and let A be the angle opposite side a.

 

There are 3 versions of the Law of Cosines:

 

a² = b²+c² - 2bccosA

 

b² =  a²+c² - 2accosB

 

c² = a²+b² - 2abcosC

 

Note that if the triangle is a right triangle (let's say that ∠C = 90°), then the 3rd version of the Law of Cosines reduces to 

a²+b² = c².