Triangle Calculator
Solve any triangle by entering three known values. Our calculator will find all remaining sides, angles, area, and perimeter, and even draw a diagram of your triangle.
Triangle Classifications
| By Sides | Description | By Angles | Description |
|---|---|---|---|
| Equilateral | All 3 sides equal | Acute | All angles < 90° |
| Isosceles | 2 sides equal | Right | One angle = 90° |
| Scalene | No sides equal | Obtuse | One angle > 90° |
How to Solve a Triangle
To "solve" a triangle means to find all its missing measurements (three sides and three angles). According to geometric principles, you need at least three pieces of information to solve a triangle, and at least one of those must be a side length.
Our calculator uses the Law of Sines and the Law of Cosines to handle all possible input combinations, including the "ambiguous case" (SSA).
Mathematical Formulas
a / sin(A) = b / sin(B) = c / sin(C)
Law of Cosines:
c² = a² + b² - 2ab cos(C)
Heron's Formula (Area):
Area = √[s(s-a)(s-b)(s-c)]
(where s = (a+b+c)/2)
Important Notes
- Triangle Inequality: For any triangle, the sum of any two sides must be greater than the third side. If this isn't met, no triangle can exist.
- Angle Sum: The sum of the three interior angles must always be exactly 180 degrees.
- Ambiguous Case (SSA): When given two sides and a non-included angle, there might be zero, one, or two possible triangles. Our calculator will identify the most likely solution.
Frequently Asked Questions
No. While three angles define the shape of the triangle, they don't define its size. There are infinitely many "similar" triangles with the same angles but different side lengths.
Heron's Formula allows you to calculate the area of a triangle using only the lengths of its three sides, without needing to know the height.
A right triangle is a triangle that has one angle measuring exactly 90 degrees. In these triangles, you can also use the Pythagorean Theorem (a² + b² = c²).
Once the area is known, the height (h) relative to a base (b) can be found using the formula: h = (2 × Area) / b.
These are abbreviations for the information given: Side-Side-Side, Side-Angle-Side, and Angle-Side-Angle. They represent the minimum requirements to uniquely define a triangle.