AZCalc.net

Math Domain Calculator • AZCalc.net

Triangle Calculator

Free Triangle Calculator. Solve any triangle using SSS, SAS, ASA, AAS, and SSA. Find angles, side lengths, area, perimeter, altitudes, medians, inradius, and circumradius.

Tool Overview & Core Functionality

Solves geometric triangles across side and angle conditions (SSS, SAS, ASA, AAS, SSA), determining side lengths, interior angles, semiperimeter, and area.

              Euclidean Trigonometry and Law of Sines / Law of Cosines:
            
              Law of Cosines: c^2 = a^2 + b^2 - 2ab*cos(C) | Heron's Area Formula

This calculator executes instantaneous, zero-latency computations strictly client-side. No financial balance, health metric, or personal chronological details are transmitted to external servers.

Admin Practical Note: Ambiguous Case (SSA)

When Side-Side-Angle Yields Two Valid Triangles

Law of Sines SSA with Acute Angle & Opp < Adj: Can produce 0, 1, or 2 distinct valid triangles depending on height comparison

Admin Practical Takeaway: AZCalc checks the altitude inequality (h = b * sin(A)) before solving SSA triangles to detect second-quadrant obtuse solutions.

Authoritative Regulatory Benchmarks & Primary Citations

Verified against statutory definitions, federal standards, and published clinical methodologies (CDC, WHO, NIH, ACOG):

National Institute of Standards and Technology (NIST): NIST Digital Library of Mathematical Functions (DLMF): Chapter 4 Elementary Trigonometric Functions
Rigorous mathematical identities for the Law of Sines, Law of Cosines, Heron's formula, and right-triangle trigonometry.

Frequently Asked Questions (Math)

What is the SSA ambiguous case in trigonometry?: When given two sides and a non-included acute angle, there may be zero, one, or two valid geometric triangles satisfying the condition.