Triangle Calculator (Heron's Formula & Angles)
Solves arbitrary triangles using Heron's formula and the Law of Cosines. Determines whether a valid triangle exists, detects right triangles, and computes interior angles in degrees and radians.
PARAMETERS(4)
LOAD VERIFIED SCENARIO
ACTIVE COMPUTATION
Triangle Area
6cm²
Right-Angled Triangle
Perimeter
12cm
Semi-perimeter (s)
6cm
Angle α (opposite a)
36.87°
Angle β (opposite b)
53.13°
Angle γ (opposite c)
90°
STEP-BY-STEP MATHEMATICAL DERIVATION
1Calculated perimeter: P = 3 + 4 + 5 = 12 cm
2Calculated semi-perimeter: s = 12 / 2 = 6 cm
3Applied Heron's Formula: Area = √(6 × (6 - 3) × (6 - 4) × (6 - 5)) = 6 cm²
4Solved angles with Law of Cosines: α = 36.87°, β = 53.13°, γ = 90°
MATHEMATICAL FORMULA & GOVERNING PRINCIPLES
s = (a + b + c) / 2, Area = √(s(s - a)(s - b)(s - c))
Heron's formula computes triangle area from the three sides without requiring height. The semi-perimeter s is half the perimeter.
FREQUENTLY ASKED QUESTIONS (FAQ)
What is the Triangle Inequality Theorem?
For any triangle, the sum of lengths of any two sides must be strictly greater than the length of the remaining side: a + b > c, a + c > b, and b + c > a.
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