EachCalculatorTriangle Calculator
Solve a triangle's angles, area, and perimeter from its three sides, or from two sides and the angle between them.
Known values
Angle A
36.87°
Angle B
53.13°
Angle C
90°
Perimeter
12
Area
6
How It Works
Three sides (SSS)
Given all three side lengths, each angle is found using the law of cosines, and the area is found using Heron's formula from the three sides.
Two sides and an included angle (SAS)
Given two sides and the angle between them, the law of cosines finds the third side first — then the triangle is solved the same way as the three-sides case.
Example Calculation
A classic 3-4-5 triangle has a right angle (90°) opposite the side of length 5, an area of 6, and a perimeter of 12.
Common Mistakes
- Entering three side lengths that can't form a real triangle (e.g. 1, 1, and 10) — the longest side must always be shorter than the sum of the other two.
- Mixing up which angle is 'included' between two sides in SAS mode — it must be the angle directly between the two given sides.
Frequently Asked Questions
- What is the law of cosines?
- For a triangle with sides a, b, c and angle C opposite side c: c² = a² + b² − 2ab·cos(C). It generalizes the Pythagorean theorem to any triangle, not just right triangles.
- What is Heron's formula?
- A formula for a triangle's area using only its three side lengths: Area = √[s(s−a)(s−b)(s−c)], where s is the semi-perimeter (half the perimeter).