Calculation Results
By Sides
Equilateral
By Angles
Acute
Side Lengths
| Side | Length |
|---|---|
| a (opposite ∠A) | 5.00 |
| b (opposite ∠B) | 5.00 |
| c (opposite ∠C) | 5.00 |
Angles
| Angle | Degrees | Radians |
|---|---|---|
| A | 60.00° | 1.05 rad |
| B | 60.00° | 1.05 rad |
| C | 60.00° | 1.05 rad |
| Sum | 180.00° | 3.14 rad |
Area & Perimeter
| Area | 10.83 |
| Perimeter | 15.00 |
| Semiperimeter | 7.50 |
Other Properties
| Inradius | 1.44 |
| Circumradius | 2.89 |
| Median to side a | 4.33 |
| Median to side b | 4.33 |
| Median to side c | 4.33 |
Triangle Facts, Theorems, and Laws
A triangle is a polygon that has three vertices. A vertex is a point where two or more curves, lines, or edges meet; in the case of a triangle, the three vertices are joined by three line segments called edges.
Pythagorean Theorem
For any right triangle: a² + b² = c²
Given a = 3, c = 5, find b:
3² + b² = 5² → 9 + b² = 25 → b² = 16 → b = 4
Law of Sines
a / sin(A) = b / sin(B) = c / sin(C) = 2R
Given b=2, B=90°, C=45°, find c:
2/sin(90°) = c/sin(45°) → c = 2 × (√2/2) × (1/1) = √2
Law of Cosines
a² = b² + c² - 2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)
Area Calculations
Base and height: Area = 1/2 × b × h
Two sides and included angle: Area = 1/2 × a × b × sin(C)
Heron's formula: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2