CALCULATOR
Triangle Area from Two Sides and Included Angle Calculator
Triangle Area from Two Sides and Included Angle. Example: Side a: 3 m, Side b: 4 m, Included angle: 90 degrees gives 6 m². Angle C is between the two supplied sides; nondegenerate ordinary Euclidean triangle. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
Angle C is between the two supplied sides; nondegenerate ordinary Euclidean triangle. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Altitude from side b equals b sin(C); halve base times altitude.
Accepted inputs: Side a: 0.001 to 10,000 m; Side b: 0.001 to 10,000 m; Included angle: 0.01 to 179.99 degrees.
How the calculation works
A=ab sin(C)/2
Worked example
With side a 3 m, side b 4 m, included angle 90 degrees, triangle area from two sides and included angle is 6 m².
Assumptions and limits
Angle C is between the two supplied sides; nondegenerate ordinary Euclidean triangle. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Altitude from side b equals b sin(C); halve base times altitude.