## Law of Cosines. Choosing your a, b and c's?

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
chiefboo
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### Law of Cosines. Choosing your a, b and c's?

Is there some convention or common sense (which I appear to lack) when it comes to choosing which sides you will assign to which variables? I assumed it didn't matter, but I've come across many cases where I come up with very different answers.

For instance, in problems where 3 sides are given I was provided 5, 11, and 9 as the length of the sides. If I say a = 11 b = 9 and c = 11 I wind up with the incorrect answer but if I use 9 for a, 5 for b and 11 c then I can get the correct answer.

Can anyone explain to me how I'm supposed to know which sides to use for a, b and c?

jg.allinsymbols
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Joined: Sat Dec 29, 2012 2:42 am
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### Re: Law of Cosines. Choosing your a, b and c's?

Is there some convention or common sense (which I appear to lack) when it comes to choosing which sides you will assign to which variables? I assumed it didn't matter, but I've come across many cases where I come up with very different answers.

For instance, in problems where 3 sides are given I was provided 5, 11, and 9 as the length of the sides. If I say a = 11 b = 9 and c = 11 I wind up with the incorrect answer but if I use 9 for a, 5 for b and 11 c then I can get the correct answer.

Can anyone explain to me how I'm supposed to know which sides to use for a, b and c?

Just identify your triangle. Law of Cosines relies on two segments and the angle between them. This law is like the pythagorean theorem but fits when the triangle is not a right-triangle.

You may have an unknown but findable angle when you are given values for all three segments of a triangle. In fact, if all three sides of the triangle are given, you can find the angles measures for all three vertices using Law of Cosines. You would need to make an equation for each angle. Yes, for this, you could have three different results: a different equation for each angle to be found.