STRATEGIES

FOR

SOLVING OBLIQUE TRIANGLES

Case 1 (Given two angles and one side) ASA or SAA

1. Find the third angle. (They add up to 180°.)

2. Use the Law of Sines to find the other two sides.

Case 2 (Given two sides and an angle opposite one of those sides) SSA

1. Use the Law of Sines to find the sine of one missing angle.

If this is greater than 1, STOP--no solutions.

2. If the number obtained in step 1 is £ 1 (call it x), then there are two possibilities for that angle: and 180° - .

3. Find both possible third angles. (They add up to 180°.) If one is negative, discard it--there is just one solution. Otherwise, there are two solutions.

4. Use the Law of Sines to find the third side for each remaining possible solution.

Case 3 (Given two sides and their included angle) SAS

1. Use the Law of Cosines to find the third side.

2. Use the Law of Sines to find the smaller remaining angle (the one opposite the smaller side), since it must be acute.

3. Find the third angle. (They add up to 180°.)

Case 4 (Given three sides) SSS

1. Use the Law of Cosines to find the largest angle first (so the remaining ones are automatically acute).

2. Use the Law of Sines to find either of the other two angles.

3. Find the third angle. (They add up to 180°.)