but they do not want to find the third side, they want to find the other angles. It will be necessary to use the Law of
Cosines to get the third side, and then use that third side to get the ratio for the triangle so the Law of Sines could be
used. Remind students to be creative when solving exercises. They should use all of their mathematical knowledge
to figure out the solution.
Triangle Labeling –Stress the labeling convention of using a capital letter for a vertex and the same letter in lower
case for the opposite side. It is especially important when using the Law of Cosines to fine an angle. Students need
to verify that they start the Law of Cosines with the side opposite of the angle they are finding.
Multiplication Before Addition –At this level, students usually faithfully follow this application of the order of
operations except, when using the Law of Cosines to fine an angle. The last term of the Law of Cosines is−2abcosC.
This is four values being multiplied together. The cosine function is new to students. They will not see it as the
representation of a number and will separate it from the other terms. Frequently, they will subtract the− 2 abfrom
thea^2 +b^2 or add it to thec^2 on the other side of the equation. Use a big multiplication symbol when writing and
using the formula. It can be written,− 2 ab∗cosC, to remind students to use the proper order of operations.
Chapter 2. Geometry TE - Common Errors