How to use it
- Pick the combination of values you know from the list.
- Enter them. Side a is opposite angle A, side b opposite B and side c opposite C.
- Read the remaining sides and angles, the area, the perimeter and the type of triangle.
Methods
| Case | Method |
|---|---|
| SSS | law of cosines gives each angle |
| SAS | law of cosines gives the third side, then the angles |
| ASA, AAS | third angle = 180° − A − B, then the law of sines |
| SSA | law of sines, sin B = b × sin A ÷ a, which can have two answers |
The area is ½ × a × b × sin C, and the perimeter is a + b + c.
The SSA case
Fix the angle A and the side b, then try to place the side a opposite A. If a is longer than or equal to b, it can only meet the base in one place. If a is shorter than b, it may meet it twice, once with an acute angle B and once with the obtuse angle 180° − B. If it is shorter than the height b × sin A, it cannot reach at all.
Worked examples
- 3, 4, 5 (SSS). The angles are 36.87°, 53.13° and 90°, the area is 6 and the triangle is scalene and right.
- 30°, 60°, side c = 10 (ASA). C = 90°, a = 5 and b = 8.66, and the area is 21.65.
- a = 5, b = 7, A = 30° (SSA). Two triangles: c = 9.63 with B = 44.43°, or c = 2.49 with B = 135.57°.
Common mistakes
- Mixing up which angle is opposite which side. Capital letters are angles, lowercase letters the sides across from them.
- Rounding too early. Rounding the middle values and then using them can shift the last digits of the answer.