Triangle solver: sides, angles and area
Pick what you know (three sides, two sides and an angle…), type the values: everything else is worked out. Angle A faces side a.
Result
6Area
- Number of possible triangles
- 1
- Side a
- 3
- Side b
- 4
- Side c
- 5
- Angle A
- 36.8699°
- Angle B
- 53.1301°
- Angle C
- 90°
- Perimeter
- 12
Inputs
- I know
- 3 sides (a, b, c)
- Angle unit
- Degrees
- Side a
- 3
- Side b
- 4
- Side c
- 5
How it is calculated
Angle sum: A + B + C = 180°.
Result
Area
- Number of possible triangles
- 1
- Side a
- 3
- Side b
- 4
How it is calculated
- Angle sum: A + B + C = 180°.
- Law of cosines: c² = a² + b² − 2ab × cos C.
- Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C.
- Area = ½ × a × b × sin C.
- With 2 sides and an angle not between them there can be 0, 1 or 2 triangles: the tool shows all of them.
Example
Sides 3, 4 and 5: angle C is 90°, the area is 6 and the perimeter 12.
Good to know
- Sides share one unit of your choice; the area is in that unit squared.
- If the values cannot make a triangle (for example 1, 2 and 3), the tool says so.
- Results are rounded on screen.
Frequently asked questions
What is this tool used for?
Pick what you know (three sides, two sides and an angle…), type the values: everything else is worked out. Angle A faces side a.
How is the result calculated?
Angle sum: A + B + C = 180°.
What should I check before using the result?
Sides share one unit of your choice; the area is in that unit squared.