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Is there any difference between using SSA or SAS for law of sines? Are they the same?

For example, assuming Capital letters are angles, opposite legs are lower case

If A= 28 degrees, b =14 and c =9(note that we do not know where the leg belong, do not refer to image for actual problem) , how do we know SAS or SSA triangle? Can we use law of signs to solve this "special case triangle" how would we begin to solve?

Harry Iguana
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  • It's SAS. Two sides and the angle in between. The steps for this are all over the internet. You start with the law of cosines. The picture you provided is a right-triangle however, and you mention 'legs'. – David P Jan 10 '22 at 22:47
  • So I am still unfamiliar with this concept, I need to start with law of cosines? I can't use sines? – Harry Iguana Jan 10 '22 at 22:55
  • https://en.wikipedia.org/wiki/Law_of_cosines – Golden_Ratio Jan 10 '22 at 23:14
  • You can only use law of sines if you know (or can find) an angle and the side opposite of it. If this were actually a right triangle then yes, as you know c and C. – David P Jan 10 '22 at 23:18

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You should probably remove the image since it conflicts with the info you have provided.

To determine if you have SSA and SAS as options you need to pick a corner and move around the triangle checking for known values. Direction doesn't matter, its a good idea to check both directions until you get the hang of it.

SSA means that you know the lengths of two consecutive sides and the angle that follows the second side.

SAS means you know the values of two sides and the angle they form together. In the case of your example, you know the values of sides b and c as well as the value of the angle that connects them so it is SAS.

DadFlex
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