If you try to do this with a unique triangle (one without two possible sets of angles and sides) your given angle and the obtuse angle you find will add up to more than 180, and so if you try to find a third angle to go with the obtuse one, your subtraction will tell you the third angle is negative, at which point you know you're going down a nonsensical mathematical road, and there weren't two possible triangles to begin with. And you find the obtuse one by subtracting the acute one from 180. It all comes from knowing that there are two angles, one obtuse and one acute, for every sine value. If you use the given angle-side pair (C and c) you will be less likely to incur error from your own rounding of angle A:īut if you know that supplementary angles share a sine value, you know that A can also be an obtuse angle with the same sine as 47.6924:Īnd again, subtract 31 (C) and the obtuse angle A from 180 to find the other possible third angle (B=16.6924) and use the Law of Sines to find the other possible third side, again using angle C and side c to avoid errors from rounding: (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangles side or angle) Law of Sines. Subtract 31 (C) and this angle (A) from 180 to find the third angle (B=101.3076) and use the Law of Sines again to find the third side.
Use the Law of Sines to get one possible angle A:
