Maths & numbers
Triangle from sides & angles
Solve a plane triangle from two sides and their included angle, or one side and two angles.
A clear answer. Here’s how.
SAS uses the cosine law in a cancellation-resistant half-angle form; remaining angles use atan2. The two-angle mode sets C=180°−A−B and uses the sine law with known side a. Reports sides, angles, area, perimeter and in/circumradii. Requires a non-degenerate Euclidean triangle; extremely disproportionate dimensions beyond reliable floating-point angular resolution are rejected. All sides use one unit.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Given measurements
- Sides b, c and included angle A
- Side b
- 4
- Side c
- 3
- Angle A (degrees)
- 90
Example result
- Side a
- 5
- Side b
- 4
- Side c
- 3
- Angle A
- 90 °
- Angle B
- 53.1301023542 °
- Angle C
- 36.8698976458 °
- Area (square units)
- 6
- Perimeter
- 12
- Inradius
- 1
- Circumradius
- 2.5