Question

State one form of the Law of Cosines and provide a trick for writing the other two forms and explain when Law of Cosines should be used to solve a triangle.

Answer 1

Solving for Angles

$\displaystyle \frac{a^2 + b^2 - c^2}{2ab} = cos∠C \\ \frac{a^2 - b^2 + c^2}{2ac} = cos∠B \\ \frac{-a^2 + b^2 + c^2}{2bc} = cos∠A$

* Do not forget to use the inverse function towards the end, or elce you will throw your answer off!

Solving for Edges

$\displaystyle b^2 + a^2 - 2ba\:cos∠C = c^2 \\ c^2 + a^2 - 2ca\:cos∠B = b^2 \\ c^2 + b^2 - 2cb\:cos∠A = a^2$

You would use this law under two conditions:

• One angle and two edges defined, while trying to solve for the third edge
• ALL three edges defined

* Just make sure to use the inverse function towards the end, or elce you will throw your answer off!

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Now, JUST IN CASE, you would use the Law of Sines under three conditions:

• Two angles and one edge defined, while trying to solve for the second edge
• One angle and two edges defined, while trying to solve for the second angle
• ALL three angles defined [of which does not occur very often, but it all refers back to the first bullet]

* I HIGHLY suggest you keep note of all of this significant information. You will need it going into the future.

I am delighted to assist you at any time.