Enter triangle information
Formula used
Angle sum: A + B + C = 180°.
Law of Cosines: c² = a² + b² − 2ab cos(C).
Law of Sines: a ÷ sin(A) = b ÷ sin(B) = c ÷ sin(C).
Right triangles: θ = sin⁻¹(opposite ÷ hypotenuse), cos⁻¹(adjacent ÷ hypotenuse), or tan⁻¹(opposite ÷ adjacent).
Coordinate distance: d = √((x₂ − x₁)² + (y₂ − y₁)²).
Heron area: Area = √(s(s − a)(s − b)(s − c)).
How to use this calculator
- Select the known triangle information.
- Choose angle and side units.
- Enter every requested value carefully.
- Select the required decimal precision.
- Press Calculate triangle.
- Review angles, sides, steps, classifications, and the diagram.
- Copy, print, or download the result.
Triangle calculation methods
SSS
SSS means all three sides are known. The calculator uses cosine rules. It then verifies the complete triangle.
SAS
SAS uses two sides and their included angle. It solves the opposite side first. Remaining angles follow from cosine rules.
ASA and AAS
These cases use two known angles. The third comes from 180 degrees. Sine rules calculate every missing side.
SSA ambiguous case
SSA may create zero, one, or two triangles. Both inverse-sine solutions require testing. Invalid angle combinations are removed automatically.
Example data
| Mode | Known values | Expected result |
|---|---|---|
| Two angles | A = 50°, B = 60° | C = 70° |
| SSS | a = 5, b = 6, c = 7 | A ≈ 44.42°, B ≈ 57.12°, C ≈ 78.46° |
| SAS | a = 8, b = 10, C = 45° | All sides and angles |
| SSA | A = 30°, a = 7, b = 10 | Two triangles may exist |
| Coordinates | A(0,0), B(4,0), C(1,3) | All three angles |
Calculation history
No saved calculations yet.
Frequently asked questions
Can this calculator find every triangle angle?
It supports common solvable triangle combinations. Valid measurements must define a triangle. Impossible inputs produce a clear warning.
Why must triangle angles total 180 degrees?
Euclidean triangles have a fixed interior sum. Every valid triangle follows this rule. The calculator verifies that total automatically.
What does SSS mean?
SSS means three side lengths are known. Cosine rules determine each angle. Triangle inequality validation happens before calculation.
What is the SSA ambiguous case?
SSA can describe two different triangles. Supplementary inverse-sine angles may both work. The calculator displays each valid solution.
Can I enter radians?
Yes, choose radians before entering angles. Results remain clearly labeled in degrees. DMS output is also provided where useful.
How do DMS inputs work?
Enter degrees, minutes, and seconds separated by spaces. For example, use 35 20 10. Minutes and seconds must stay below sixty.
Can coordinates form an invalid triangle?
Yes, three points may be collinear. Such points have zero triangle area. The calculator rejects that coordinate combination.
Why is the diagram not perfectly scaled?
The diagram fits available screen space. Labels remain readable on smaller devices. Calculated numbers remain the authoritative measurements.
Can results be downloaded?
Yes, export results as CSV or PDF. Printing is also available. Copied text includes the main calculation result.