Triangle Sides Calculator | Geometry Solver, Graph & Exports

Triangle Sides Calculator Form

Choose a solving case, enter the known measurements, and press calculate. Results appear above this form under the header.

Select solving mode

Side a

Side b

Side c

Side a

Side b

Included angle C (degrees)

Angle A (degrees)

Angle B (degrees)

Known side c

Leg a

Leg b

Hypotenuse c

Example Data Table

Case	Known Inputs	Computed Highlights
SSS	a = 3, b = 4, c = 5	Area = 6.0000, Perimeter = 12.0000, Angle C = 90.0000°
SAS	a = 7, b = 9, C = 60°	c = 8.1854, Area = 27.2798, Triangle type = Acute scalene
ASA / AAS	A = 50°, B = 60°, c = 8	a = 6.5217, b = 7.3728, C = 70.0000°
Right triangle	a = 5, b = 12	c = 13.0000, Area = 30.0000, Angle C = 90.0000°

Formula Used

Law of Cosines

For SAS and SSS work:
c² = a² + b² − 2ab cos(C)
A = cos⁻¹((b² + c² − a²) / 2bc)
B = cos⁻¹((a² + c² − b²) / 2ac)

Law of Sines

For ASA and AAS solving:
a / sin(A) = b / sin(B) = c / sin(C)
After finding C = 180° − A − B, solve the unknown sides directly.

Right Triangle Rule

When C = 90°:
c² = a² + b²
This finds the missing side when two right-triangle sides are known.

Area and Perimeter

Perimeter = a + b + c
s = (a + b + c) / 2
Area = √(s(s − a)(s − b)(s − c))
Height to side c = 2 × Area / c

Graph Coordinates

The graph places side c on the x-axis. The third vertex is built from:
x = (b² + c² − a²) / 2c
y = √(b² − x²)

How to Use This Calculator

Select the triangle case that matches your known values.
Enter only positive side lengths and valid degree measures.
For right-triangle mode, treat c as the hypotenuse.
Press Calculate Triangle to show results above the form.
Review sides, angles, area, perimeter, classifications, and the Plotly graph.
Use the export buttons in the result section to download CSV or PDF output.

Frequently Asked Questions

1. What triangle cases can this page solve?

It solves SSS, SAS, ASA or AAS, and right-triangle cases. Each option uses standard geometry rules to compute missing sides, angles, area, perimeter, and related measures.

2. Why do some side values fail validation?

A valid triangle must satisfy the triangle inequality. The sum of any two sides must exceed the third side. If not, the shape cannot close into a triangle.

3. Why is side c used as the base in the graph?

Using side c as the base creates a stable coordinate layout. It keeps the plotted triangle easy to read while preserving correct side lengths and angles.

4. Can this calculator handle right triangles?

Yes. Choose the right-triangle mode and enter any two sides, using c as the hypotenuse. The page then computes the missing side and acute angles automatically.

5. Why are the displayed values rounded?

Rounded output improves readability and keeps tables clean. Internally, calculations use standard floating-point math, so tiny differences may appear when compared with hand-rounded steps.

6. When should I use SAS instead of ASA or AAS?

Use SAS when you know two sides and the included angle between them. Use ASA or AAS when you know two angles and one side.

7. What do the CSV and PDF buttons export?

CSV exports a compact results table with inputs and solved values. PDF captures the result section, making it useful for reports, homework checks, or printable records.

8. Does it work for obtuse triangles too?

Yes. The formulas support acute, right, and obtuse triangles as long as the entered values describe a valid triangle. The angle classification identifies the triangle type.