The Law of CosinesOn this web page you can validate for yourself the Law of Cosines
that you studied in Lesson 8.7 of Discovering Advanced Algebra: An
Investigative
Approach. You can think of the Law of Cosines as a modified
Pythagorean relationship.
Sketch
This sketch shows triangle ABC and the measurements of its
angles and sides. Drag any of the vertices to change the triangle's
size and shape, or press Make Right
Triangle to change it to a right
triangle. The values of c^{2}, a^{2}, b^{2},
2ab cos C, and a^{2} + b^{2}
– 2ab cos C
are calculated for you.
Investigate
 What do you observe about c^{2} and a^{2}
+ b^{2} – 2ab cos C for any triangle? How
does this validate the Law of Cosines (with respect to angle C)?
 What happens to the Law of Cosines when angle C is right?
 What can you say about 2ab cos C when angle C
is acute? When angle C is obtuse?
If you'd like to algebraically derive the Law of Cosines, go to the Law of Cosines page for Discovering
Geometry
and look at the second sketch on the page.
