Triangle Solver Triangle Trig Calculator

Solve triangle dimensions with smart trigonometric methods and checks. Enter mixed known values, view geometry, and export neat summaries. Great for students solving hard triangle questions accurately.

Triangle Input Form

Enter any valid three values with at least one side. The solver supports SSS, SAS, ASA, AAS, and SSA combinations.

Triangle Plot

The graph draws the primary solved triangle using Cartesian coordinates built from the solved side lengths.

Example Data Table

Case	Input Values	Main Method	Sample Result
SSS	a = 7, b = 8, c = 9	Law of Cosines	Angles are solved from all three sides.
SAS	b = 5, c = 9, A = 40°	Cosines then Sines	Missing side and remaining angles are found.
ASA	A = 50°, B = 60°, c = 11	Angle sum then Sines	Third angle and two sides are solved.
SSA	a = 10, b = 8, A = 35°	Ambiguous sine case	One or two valid triangles may exist.

Formula Used

1) Angle Sum Rule

A + B + C = 180°

2) Law of Sines

a / sin(A) = b / sin(B) = c / sin(C)

3) Law of Cosines


a² = b² + c² - 2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)

4) Heron’s Formula


s = (a + b + c) / 2
Area = √[s(s-a)(s-b)(s-c)]

5) Extra Measures


Perimeter = a + b + c
Height to side a = 2 × Area / a
Inradius = Area / s
Circumradius = abc / (4 × Area)
Median to side a = 0.5 × √(2b² + 2c² - a²)

How to Use This Calculator

Enter any three valid triangle measures.
Include at least one known side length.
Use positive values only for every side.
Keep each entered angle below 180 degrees.
Click Solve Triangle to calculate the missing values.
Review the result cards above the form.
Check the graph to see the triangle shape.
Use the CSV or PDF buttons to export the results.

FAQs

1. What triangle cases does this solver support?

It supports SSS, SAS, ASA, AAS, and SSA. The SSA case is checked carefully because it can create zero, one, or two valid triangles depending on the entered values.

2. Why must I enter at least one side?

Angles alone only describe shape, not size. One side sets the scale, allowing the calculator to determine the full triangle dimensions, perimeter, area, radii, and graph coordinates.

3. What happens if my values do not form a triangle?

The tool returns an error message. Examples include impossible angle sums, invalid angle ranges, or side lengths that break the triangle inequality rule.

4. Can the calculator detect ambiguous SSA triangles?

Yes. When SSA produces two valid triangles, both are shown in separate result blocks. This helps you compare the different angle and side combinations.

5. How is the triangle graph created?

The calculator places one side on the x-axis, then computes the third vertex using the solved side lengths. That coordinate set is passed into Plotly for drawing.

6. Does this calculator work for right triangles too?

Yes. Right triangles are included automatically. The classification section marks the triangle as right whenever one solved angle is 90 degrees.

7. What extra outputs are included besides sides and angles?

It also shows area, perimeter, semiperimeter, heights, medians, inradius, circumradius, case type, and side-angle classification for a fuller trigonometric analysis.

8. Can I export the solved values?

Yes. Use the CSV button for spreadsheet-friendly numeric data, or the PDF button for a formatted report that is easy to share or print.