Triangle Calculator
How to Use the Triangle Calculator
Triangle Calculation Methods
There are several methods to solve a triangle, depending on which parts of the triangle you know:
- SSS (Three Sides): When you know all three sides of the triangle.
- SAS (Two Sides and Included Angle): When you know two sides and the angle between them.
- ASA (Two Angles and Included Side): When you know two angles and the side between them.
- AAS (Two Angles and Non-included Side): When you know two angles and a side that is not between them.
- SSA (Two Sides and Non-included Angle): When you know two sides and an angle that is not between them.
Step-by-Step Instructions
- Select the calculation type based on what information you have.
- Enter the known values in the input fields.
- Click the "Calculate" button.
- View the results, including all sides, angles, area, and perimeter.
Triangle Formulas
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines: c² = a² + b² - 2ab·cos(C)
Area: Area = (1/2) × base × height
Heron's Formula for Area: Area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2
Perimeter: Perimeter = a + b + c
Common Triangle Calculations
Right Triangle
A right triangle has one angle equal to 90°. The Pythagorean theorem applies: a² + b² = c², where c is the length of the hypotenuse (the side opposite to the right angle).
Equilateral Triangle
An equilateral triangle has all sides of equal length and all angles equal to 60°. If s is the side length, the area is (√3/4) × s².
Isosceles Triangle
An isosceles triangle has two sides of equal length and two angles of equal measure.
FAQ
What is the sum of angles in a triangle?
The sum of all internal angles in a triangle is always 180 degrees (or π radians).
Can all combinations of sides form a triangle?
No. For a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.
What is the SSA ambiguous case?
The SSA (two sides and non-included angle) case can be ambiguous, meaning it may result in either zero, one, or two possible triangles, depending on the specific values.
How accurate is this calculator?
This calculator performs computations with high precision but rounds the displayed results to two decimal places for readability.