What is Triangle Geometry?

Triangle geometry involves the mathematical study of triangles, their properties, and relationships between sides and angles. Our triangle calculator solves various triangle problems including area, perimeter, and angle calculations.

Types of Triangle Calculations

• Three Sides (SSS): Calculate angles and area from three side lengths
• Two Sides and Angle (SAS): Calculate remaining sides and angles
• Base and Height: Calculate area using base and perpendicular height
• Right Triangle: Calculate hypotenuse and properties of right-angled triangles

Triangle Properties and Formulas

Area Formulas

• General: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
• Base and height: Area = (base × height) ÷ 2
• Right triangle: Area = (leg₁ × leg₂) ÷ 2

Angle Sum Property

The sum of angles in any triangle is always 180 degrees.

Triangle Inequality Theorem

For any triangle, the sum of any two sides must be greater than the third side.

Laws of Triangles

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C) = 2R (where R is the circumradius)

Law of Cosines

c² = a² + b² - 2ab cos(C)

Pythagorean Theorem

For right triangles: c² = a² + b²

Types of Triangles

• Equilateral: All sides equal, all angles 60°
• Isosceles: Two sides equal, two angles equal
• Scalene: All sides different, all angles different
• Right: One angle is 90°
• Acute: All angles less than 90°
• Obtuse: One angle greater than 90°

Practical Applications

• Architecture: Roof design, structural calculations
• Navigation: Distance and direction calculations
• Physics: Force vector analysis
• Engineering: Stress analysis, material design
• Surveying: Land measurement and mapping