CALCULATOR
Triangle Opposite Side from Two Sides and Included Angle Calculator
Triangle Opposite Side from Two Sides and Included Angle. Example: Side a: 3 m, Side b: 4 m, Included angle: 90 degrees gives 5 m. Included angle strictly between0 and180; return only opposite side, no ambiguous SSA solve. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
Included angle strictly between0 and180; return only opposite side, no ambiguous SSA solve. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Cosine law rewritten using1-cosC=2sin²(C/2) to avoid subtraction of near-equal squares.
Accepted inputs: Side a: 0.1 to 1,000 m; Side b: 0.1 to 1,000 m; Included angle: 1 to 179 degrees.
How the calculation works
c=√((a-b)²+4ab sin²(C/2))
Worked example
With side a 3 m, side b 4 m, included angle 90 degrees, triangle opposite side from two sides and included angle is 5 m.
Assumptions and limits
Included angle strictly between0 and180; return only opposite side, no ambiguous SSA solve. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Cosine law rewritten using1-cosC=2sin²(C/2) to avoid subtraction of near-equal squares.