Triangle Calculator
Enter the three side lengths of a triangle to instantly calculate its area, perimeter, and all three internal angles.
Utilizes Heron's Formula and the Law of Cosines to solve the geometry.
The Comprehensive Guide to Complete Triangle Solver (Sides to Angles)
What is a Complete Triangle Solver (Sides to Angles)?
The Triangle Calculator is a comprehensive geometry solver. Given only the lengths of a triangle's three sides, it automatically derives the area, perimeter, and the exact degrees of all three internal angles.
It also universally identifies the triangle's formal classification (Equilateral, Isosceles, Scalene) and instantly flags invalid dimensions that violate the laws of geometric physics.
The Mathematical Formula
Where b is base and h is vertical height.
Calculation Example
Let's input the famous standard integer "3-4-5 Triangle" (Sides: a=3, b=4, c=5).
- Perimeter: 3 + 4 + 5 = 12.
- Area: The calculator applies Heron's formula to reveal the exact area is 6.
- Angles: The Law of Cosines calculates the angles as 36.87°, 53.13°, and a perfect 90°.
- Classification: Because all three sides differ and one angle is exactly 90 degrees, it is correctly identified as a Scalene (Right-Angled) triangle.
Strategic Use Cases
- Carpentry & Construction: Ensuring a newly built frame, ramp, or staircase is perfectly "square" (90 degrees) by verifying the diagonal cut matches a valid right-triangle hypotenuse.
- Land Surveying: Calculating the exact internal angles of an uneven triangular plot of land when only the outer border lengths are known.
- Trigonometry Homework: Instantly verifying manual, hand-written calculations for the Law of Sines/Cosines and Heron's Formula.
Frequently Asked Questions
Why does the calculator say my triangle is 'Invalid'?
Because you violated the Triangle Inequality Theorem. Stated simply: the two shortest sides of a triangle MUST add up to be longer than the longest side. If they don't, the two short sides physically couldn't connect to close the shape. (E.g., sides of 2, 2, and 100 cannot form a triangle).
What do Scalene, Isosceles, and Equilateral mean?
Scalene means all 3 sides are different lengths. Isosceles means exactly 2 sides are the same length. Equilateral means all 3 sides are perfectly equal.
Why do the internal angles always add up to 180 degrees?
According to the fundamental Euclidean laws of geometry, the three interior angles of ANY flat, 2-dimensional triangle will always sum to exactly 180 degrees, without exception.
Related Strategic Tools
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