SOLUTION: The lengths of the sides of triangle ABC are AB=6, BC=4, and CA=5, then cos A=?

The law of cosines for when you have all three sides and
no angle given is

                 (one ADJACENT side)² + (other ADJACENT side)² - (OPPOSITE)²
cosine(ANGLE) = -------------------------------------------------------------
                      2(one ADJACENT side)(other ADJACENT side)


The ANGLE we want to find the cosine of is A.
One ADJACENT side to angle A is AB which is 6 in length.
The other ADJACENT side to angle A is CA which is 5 in length.
The OPPOSITE side is the side across the triangle
from angle A, which is BC, 4 in length.

 






Edwin