The SSS (Side-Side-Side) Triangle Calculator is the fundamental solver for when you have measured all three boundary lengths of a triangle but know none of the angles. Using the powerful Law of Cosines, it reverse-engineers the shape to provide every missing angle, plus the area and perimeter.
Features
Complete Solution: Finds Angles A, B, and C from just side lengths.
Validity Check: Automatically enforces the Triangle Inequality Theorem ($a+b>c$) to prevent impossible shapes.
Heron’s Formula: Calculates the area without needing height.
Scaled Drawing: Visualizes the resulting triangle based on your inputs.
How to Use This Calculator
Measure Sides: Gather the lengths of a, b, and c.
Input: Enter these three values into the fields.
Solve: Click to generate the angles and area.
Verify: Check the generated visual to ensure it matches your expectations.
Formulas
The calculator uses the following mathematical principles:
Law of Cosines (for Angle): $$ \cos C = \frac{a^2 + b^2 – c^2}{2ab} $$
Heron’s Formula (Area): $$ \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} $$
Perimeter: $$ P = a + b + c $$
Practical Applications
Carpentry: verifying corner angles when only tape measure lengths are available.
Fabrication: Creating templates for welding or sheet metal work.
Land Property: Calculating the area of a triangular lot given survey stake distances.
Tips for Success
Longest Side: The largest angle is always opposite the longest side.
Impossible Triangles: If one side is longer than the other two combined, no triangle can close. The calculator will warn you.
Units: The unit of length implies the unit of area (e.g., input meters -> output square meters).
Frequently Asked Questions (FAQ)
Can I solve for just one angle?
This tool solves for all three automatically, so you pick the one you need.
Is the result unique?
Yes, SSS uniquely defines a rigid triangle shape (congruence).
Final Words
Turn measurements into geometry. The SSS Triangle Calculator is the reliable workhorse for converting raw distance data into a complete understanding of a triangle’s form.
