Triangle Area (Two Sides and Included Angle)
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
Half base times height, without ever measuring the height: if two sides pinch an angle C between them, then b sin C is the perpendicular height on base a, so A = ½ab sin C. Land surveyors use it constantly — two fence lines of 30 m and 42 m meeting at 75° enclose ½ × 30 × 42 × sin 75° ≈ 608 m² of triangular lot. The angle is not solvable here: C and its supplement 180° − C share the same sine, so the same area fits two different triangles.
Triangle Area (Two Sides and Included Angle)
Where
- = Triangle area
- = Side a
- = Side b
- = Included angle between a and b
Missing one of these? Work it out first, then come back
- Triangle area — Triangle Area from Two Vectors, Area of a Circle
- Side a — Law of Sines, Trapezoid Area
- Side b — Law of Sines, Trapezoid Area
- Included angle between a and b — Law of Cosines, Dot Product from Magnitudes and Included Angle