Quadratic Equation Solver (ax² + bx + c = 0)
About Triangle Calculator
The Universal Oblique & Right Triangle Solver calculates unknown sides, interior angles, semi-perimeter ($s$), area (via Heron's formula $A = \sqrt{s(s-a)(s-b)(s-c)}$ and SAS $\frac{1}{2}ab\sin C$), inradius ($r$), circumradius ($R$), and medians using the Law of Sines and Law of Cosines.
How to Use Triangle Calculator
Step 1
Select your known inputs combination (SSS, SAS, ASA, AAS, or SSA).
Step 2
Enter the known side lengths and angle degrees.
Step 3
Review computed side lengths, angles, area, inradius, and circumradius.
Step 4
Click "Copy Triangle Solution".
Practical Use Cases for Triangle Calculator
Surveying, Triangulation & Land Topography
Compute boundary distances and field acreage from boundary GPS coordinate bearings and angle-side-angle (ASA) survey measurements.
Roof Truss & Structural Timber Framing Carpentry
Determine rafter lengths, peak pitch angles, and timber bevel angles using Side-Side-Side (SSS) and Side-Angle-Side (SAS) rules.
Input & Output Examples
Solving Triangle with Sides 7, 8, 9 (SSS)
Sides: `a = 7`, `b = 8`, `c = 9`
Area: `26.8328` (Heron's Formula) | Angles: `A = 48.19°`, `B = 58.41°`, `C = 73.40°` | Perimeter: `24.0` | Inradius: `2.236`
Key Features & Performance
- ✓Input Configurations: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), SSA (Ambiguous Case Solver).
- ✓Area Algorithms: Heron's Formula, Base $\times$ Height / 2, SAS Trigonometric Area Formula.
- ✓Ambiguous SSA Case Detector: identifies when zero, one, or two distinct valid triangles exist.
- ✓100% Client-Side geometry engine.
- ✓1-Click Copy full triangle geometric report.
Key Terminology & Definitions
Heron's Formula
A formula calculating the area of any triangle from the lengths of its three sides: $A = \sqrt{s(s-a)(s-b)(s-c)}$ where $s = (a+b+c)/2$.
Law of Cosines
A general trigonometric relationship relating the sides and cosine of an angle: $c^2 = a^2 + b^2 - 2ab\cos C$.