Triangle Calculator & Universal Trigonometric Solver

1. The SSA (Side-Side-Angle) Ambiguous Case Catastrophe When given two sides and a non-included angle, blind calculators often return only a single solution. If the opposite side $a$ is shorter than adjacent side $b$ but longer than the perpendicular altitude ($b \sin A < a < b$), TWO completely valid, geometrically distinct triangles exist—one acute and one obtuse. Ignoring the second solution leads to catastrophic engineering errors in surveying and truss design.

2. The Triangle Inequality Violation Three positive numbers do not automatically make a triangle. By Euclid's Triangle Inequality Theorem, the sum of any two sides must strictly exceed the third ($a + b > c$). Attempting to construct a triangle with sides 4, 6, and 12 is mathematically impossible because the two shorter lengths cannot bridge the gap.

3. IEEE-754 Floating-Point Arccosine Domain Crash (NaN) In digital computation, rounding inaccuracies in the Law of Cosines can calculate cos(C) as 1.0000000000000002 for near-collinear triangles. Because Math.acos() is mathematically defined strictly on the interval [-1, 1], an unclamped value instantly returns NaN and crashes client-side scripts. Clamping via Math.min(1, Math.max(-1, cosVal)) is mandatory.

4. Degree vs. Radian Conversion Mismatch JavaScript native Math.sin(), Math.cos(), and Math.tan() functions accept angles solely in radians, while human users almost universally input degrees. Forgetting to multiply degrees by (π / 180) or forgetting to convert inverse trigonometric outputs back via (180 / π) produces completely chaotic geometric dimensions.

5. The Law of Sines Obtuse Angle Blindspot The inverse sine function arcsin(x) only returns values between -90° and +90°. If a triangle possesses an obtuse angle (> 90°), using the Law of Sines to solve for that largest angle will falsely return its acute supplement (180° - θ). The Law of Cosines must always be used to solve for the largest angle first because arccosine uniquely spans 0° to 180°.