Triangle Calculators
Professional online calculators for all types of triangle calculations
Special Triangle Types
Equilateral Triangle
All sides equal - calculate area, perimeter and all properties
Isosceles Triangle (a = b)
Two equal sides - calculate all triangle parameters
Right Triangle (2 Sides) (∠ = 90°)
Right triangle with two known sides - apply Pythagorean theorem
Right Triangle (Side + Angle)
Right triangle with one known side and one angle
Isosceles Right Triangle (45°-45°-90°)
45°-45°-90° triangle with two equal legs
Area Calculations
Area from Base and Height (A = ½bh)
Classic area calculation using base and height
Area from 2 Sides and 1 Angle (A = ½ab sin(C))
Area calculation using sine rule with two sides and included angle
Area from 1 Side and 2 Angles
Area calculation from one side and two adjacent angles
Triangle, Incircle (3 Sides) (Heron)
Heron's formula for area calculation from all three side lengths
Advanced Functions
Triangle Vertices (3 Points)
Complete analysis of triangle with three given coordinate points
Bisector of a Triangle
Calculate medians and centroid of triangles
About Triangle Geometry
Triangle geometry forms the foundation of mathematics and finds practical application in:
- Architecture - Structural frameworks, roof construction
- Engineering - Truss systems, mechanical design
- Surveying - Triangulation, land measurement
- Navigation - GPS systems, positioning
- Computer Graphics - 3D modeling, rendering
- Education - Trigonometry learning
Fundamental Triangle Formulas
Area Calculations
Base/Height: A = ½·b·h
Sine: A = ½·a·b·sin(C)
Sine: A = ½·a·b·sin(C)
Heron's Formula
s = (a+b+c)/2
A = √(s(s-a)(s-b)(s-c))
A = √(s(s-a)(s-b)(s-c))
Pythagorean Theorem
Right triangle: c² = a² + b²
Legs: a, b; Hypotenuse: c
Legs: a, b; Hypotenuse: c
Trigonometric Laws
Sine: a/sin(A) = b/sin(B) = c/sin(C)
Cosine: c² = a² + b² - 2ab·cos(C)
Cosine: c² = a² + b² - 2ab·cos(C)
Tip: The sum of angles in any triangle is always 180°.
For right triangles, the Pythagorean theorem applies.
Practical Application Examples
Architecture & Construction
- Roof Structures: Rafter length calculations
- Trusses: Static load calculations
- Staircases: Angle of inclination
Engineering & Technology
- Mechanical Engineering: Support structures
- Surveying: Triangulation methods
- Navigation: Position determination
Science & Research
- Astronomy: Distance measurement
- Physics: Force decomposition
- Geodesy: Land surveying
Computer Graphics & Design
- 3D Graphics: Polygon meshes
- Game Design: Collision detection
- CAD: Technical drawings
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Quick Reference
½bh
Area
a+b+c
Perimeter
c²=a²+b²
Pythagoras
½ab sin(C)
Sine Area
∑α = 180°
Angle Sum
Triangle Types
Equilateral: All sides equal (60°-60°-60°)
Special
Isosceles: Two equal sides
Common
Right: One 90° angle
Popular
Scalene: All sides different
General
Calculation Methods
Basic Formulas: Area = ½×base×height, Perimeter = a+b+c
Trigonometry: Law of sines and cosines for complex calculations
Special Cases: Pythagorean theorem for right triangles
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