Triangle area from two sides and included angle
Enter two sides and the angle between them in degrees to get the area and the third side.
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How to use it
- Enter side a, side b, included angle and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Area = ½ × a × b × sin(C) and third side c = √(a² + b² − 2ab × cos(C)), where C is the included angle.
Example
Inputs: Side a = 5, Side b = 7, Included angle = 30 °, Length unit = Centimeters (cm). Result: Area: 8.75 cm²; Third side: 3.6576 cm; Perimeter: 15.6576 cm.
Limits and caveats
- The angle must be the one between the two sides you entered, not one opposite either side.
- The angle is in degrees, not radians.
Questions about this tool
What is the SAS triangle area formula?
Area equals half the product of the two sides times the sine of the angle between them.
What if the angle is 90 degrees?
sin 90° is 1, so the area becomes half the product of the two sides, the familiar right triangle formula.
How is the third side found?
By the law of cosines: c² = a² + b² − 2ab × cos(C).