How to use
- Fill in any three of the six boxes — sides a, b, c or angles A, B, C in degrees — and leave the rest empty.
- Angle A is opposite side a, and likewise for B and C.
- The full set of sides and angles, the area, perimeter and type appear on the right, or a message if no triangle fits.
Options explained
- Three sides (SSS)
- The law of cosines gives the angles. Any two sides must add up to more than the third.
- Two sides and the included angle (SAS)
- The law of cosines gives the third side, then the other two angles.
- Two angles and a side (ASA, AAS)
- The third angle is 180° minus the other two, then the law of sines gives the remaining sides.
- Two sides and a non-included angle (SSA)
- There may be two solutions, one or none; when there are two, both are shown.
Example
With a = 7, b = 9 and the included angle C = 60°:
- c = √(7² + 9² − 2 × 7 × 9 × cos 60°) ≈ 8.1854
- A ≈ 47.78°, B ≈ 72.22°
- Area = ½ × 7 × 9 × sin 60° ≈ 27.2798
Frequently asked questions
How do I find the angles from three sides?
Use the law of cosines, cos A = (b² + c² − a²) ÷ 2bc. For sides 3, 4 and 5 the largest angle is 90°, so it is a right triangle.
Why can't I enter just three angles?
Three angles fix the shape but not the size — the triangle can be scaled up or down — so at least one side is needed.
Why are there two answers?
With two sides and an angle opposite one of them, the other side can swing to two positions, giving one acute and one obtuse triangle. This is the ambiguous case of the law of sines.
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