Triangle Calculator
Input Triangle Data
Results
| Metric | Solution 1 |
|---|---|
| Side a | — |
| Side b | — |
| Side c | — |
| Angle A | — |
| Angle B | — |
| Angle C | — |
| Area | — |
| Perimeter | — |
| Heights (h_a, h_b, h_c) | — |
| Triangle Type | — |
How to Use This Triangle Calculator
A general triangle has six pieces—three sides and three angles—but you only get three inputs on most homework diagrams. Pick the layout that matches your givens, enter the three known values (at least one must be a side length), and the tool solves the rest including area, perimeter, heights, and triangle type.
- Select Given Information. Choose SSS, SAS, ASA, AAS, or SSA from the dropdown—the form swaps to the matching three fields.
- Enter positive dimensions. Side lengths must be greater than zero. Angles are in degrees; in SAS and SSA, angle C or angle A is the angle opposite the first listed side where noted in the form.
- Press Calculate. The results table lists all sides, angles, area, perimeter, heights, and triangle classification.
- Watch for SSA warnings. Side-Side-Angle can produce two valid triangles—the table adds a second solution column when that happens.
For a right triangle with two legs known, the Pythagorean Theorem Calculator is faster. For flat area from base and height only, try the Area Calculator triangle tab.
Triangle Formulas and Practical Applications
Solving a triangle means finding every missing side and angle from partial data—roof truss layout, CAD triangulation, or a trig worksheet all use the same two laws plus the fact that interior angles sum to 180°.
Law of Sines
a / sin(A) = b / sin(B) = c / sin(C)
Use when you know angle pairs with a side—ASA, AAS, and the SSA branch. Each side sits opposite its matching angle label.
Law of Cosines
c² = a² + b² − 2ab cos(C)
SSS and SAS modes lean on this generalization of the Pythagorean theorem. When all three sides are known, rearrange to recover angles via inverse cosine.
Area, perimeter, and heights
A = √(s(s − a)(s − b)(s − c)) where s = (a + b + c) / 2
Heron's formula runs after sides are locked in. Heights follow h = 2A / base for each side as base. Perimeter is simply a + b + c.
Ambiguous SSA case
Two sides plus a non-included angle can fit zero, one, or two triangles—sine repeats for acute and obtuse mates. When h < a < b (height from the given angle), the tool shows both solutions and flags the ambiguous case.
Standard Units and Conversion Tables
Side lengths share one unit; angles are degrees. Area is square units of the side length; perimeter matches the side unit.
| Input | Output unit |
|---|---|
| Sides (e.g. ft) | Perimeter in ft; area in ft² |
| Angles | Degrees (°) |
| Heights | Same unit as sides |
Browse math calculators for distance, slope, and circle tools that complement triangle work.
Frequently Asked Questions
How does the triangle calculator work?
Choose SSS, SAS, ASA, AAS, or SSA, enter three givens, and press Calculate. The engine applies Law of Sines, Law of Cosines, and the 180° angle rule, then computes area via Heron's formula.
What is the ambiguous SSA case?
SSA may yield two triangles. When both exist, Solution 1 and Solution 2 columns appear with a yellow warning banner at the top of the results.
How is triangle area calculated?
Heron's formula with semiperimeter s. Heights are derived from 2A / side for each base.
Why must angles sum to less than 180°?
In ASA and AAS, two given angles must leave room for a third positive angle. Inputs where A + B ≥ 180° are rejected.
What triangle types are reported?
Combined labels like "Right Scalene" or "Acute Isosceles" describe angle and side symmetry after the solve completes.
Disclaimer. RapidRatio is informational only—not structural or surveying advice. Verify load paths and field measurements with qualified professionals.