Triangle Properties Calculator
Enter the lengths of the three sides of a triangle to calculate its perimeter, area, angles, and determine its type.
Understanding the Triangle Calculator
A triangle calculator is a powerful tool for quickly determining various properties of a triangle based on given input parameters. This specific calculator focuses on the "Side-Side-Side" (SSS) case, where you provide the lengths of all three sides (A, B, and C) of the triangle.
What it Calculates:
- Perimeter: The total length of the boundary of the triangle, calculated by summing the lengths of its three sides.
- Area: The amount of two-dimensional space enclosed by the triangle. For the SSS case, this is typically calculated using Heron's formula.
- Angles: The measure of the interior angles (Angle A opposite Side A, Angle B opposite Side B, and Angle C opposite Side C) are calculated using the Law of Cosines.
- Triangle Type: The calculator identifies if the triangle is Equilateral (all sides equal), Isosceles (two sides equal), Scalene (all sides different), and also if it's a Right-angled triangle (one angle is 90 degrees).
How the Calculations Work:
1. Perimeter:
The perimeter (P) is simply the sum of the lengths of the three sides:
P = Side A + Side B + Side C
2. Area (Heron's Formula):
Heron's formula is used to find the area of a triangle when the lengths of all three sides are known. First, the semi-perimeter (s) is calculated:
s = (Side A + Side B + Side C) / 2
Then, the Area (A) is:
Area = √(s * (s - Side A) * (s - Side B) * (s - Side C))
3. Angles (Law of Cosines):
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. To find Angle A (opposite Side A):
cos(A) = (Side B² + Side C² - Side A²) / (2 * Side B * Side C)
Similarly for Angle B and Angle C. The resulting cosine value is then converted back to an angle in degrees using the inverse cosine function (arccos).
4. Triangle Type:
- Equilateral: All three sides are equal (Side A = Side B = Side C).
- Isosceles: Exactly two sides are equal (e.g., Side A = Side B, but not Side C).
- Scalene: All three sides have different lengths.
- Right-angled: If the square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean theorem: a² + b² = c²), then the triangle is right-angled. This check is performed with a small tolerance for floating-point precision.
Important Considerations:
For a valid 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. If your inputs do not satisfy this condition, the calculator will inform you that a valid triangle cannot be formed.
Example Usage:
Let's say you have a triangle with sides of length 3, 4, and 5 units. This is a classic example of a right-angled triangle.
- Side A: 3
- Side B: 4
- Side C: 5
Upon calculation, you would find:
- Perimeter: 12.00 units
- Area: 6.00 square units
- Angle A: 36.87 degrees
- Angle B: 53.13 degrees
- Angle C: 90.00 degrees
- Type: Scalene, Right-angled Triangle
This calculator is a useful tool for students, engineers, architects, and anyone working with geometric problems involving triangles.