How to use this calculator
- Identify the measurements labelled Angle α, Angle β. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
Angle α = 50; Angle β = 60
Worked example
For Angle α = 50°, Angle β = 60°, applying the displayed relationship gives third angle γ ≈ 70°. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
In Euclidean geometry the interior angles total 180 degrees. Any side may be called the base; the matching height must be perpendicular to that base or its extension. Three side lengths determine a triangle up to reflection and rigid motion.
The included angle in SAS lies between the two entered sides. A sloping side is usually not the perpendicular height. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.