I was doing my Geometry EOC review which led me to a question asking me to "List the sides of the triangle in order from SHORTEST to LONGEST". This made me confused because the only information given was three angles, the measure of angles A(59), B(77), and C(44). How should I attempt to solve a problem like this? Thanks.
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so you cannot give an exact number as that triangle can be infinitely big or infinitely small and the angles are preserved. Instead you can compare the ratio of the sides by looking at the angles opposite. The bigger the angle opposite, the longer the side. So you can simply say AC is the longest side, then BC, and so on.
If you need to get an actual ratio of one side to the other, you can assume one side equals ‘x’, then use the cosine rule and/or the sine rule to complete the other lengths in terms of x. However given the angles involved these won’t be nice neat numbers and so believe the first part is what you’re looking for.