Triangle Calculator
Understanding Triangles: A Comprehensive Guide
What is a Triangle Calculator?
A triangle calculator is a specialized tool that helps solve various triangle-related problems. Our calculator handles multiple calculation methods including SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), and right triangle calculations, making it useful for geometry, trigonometry, and real-world applications.
Key Features of Our Triangle Calculator
- Multiple calculation methods: SSS, SAS, ASA, and right triangle
- Comprehensive results: All sides, angles, area, perimeter, heights
- Triangle types: Identifies if triangle is scalene, isosceles, or equilateral
- Right triangle features: Special calculations for right triangles
- Visual representation: Shows triangle shape based on inputs
Triangle Formulas Used
Law of Cosines
c² = a² + b² – 2ab cos(C)
Used to find a side when two sides and the included angle are known (SAS)
Law of Sines
a / sin(A) = b / sin(B) = c / sin(C)
Used to find sides/angles when two angles and a side are known (ASA)
Pythagorean Theorem
a² + b² = c²
Used for right triangles to find any missing side
Types of Triangles
Triangles can be classified by their sides and angles:
By Sides
- Equilateral: All sides equal, all angles 60°
- Isosceles: Two sides equal, two angles equal
- Scalene: All sides and angles different
By Angles
- Acute: All angles < 90°
- Right: One angle = 90°
- Obtuse: One angle > 90°
Practical Applications of Triangle Calculations
Triangle geometry is used in many real-world situations:
- Construction: Roof framing, bridge design
- Navigation: Triangulation for GPS and mapping
- Art and design: Creating perspective and composition
- Physics: Force vector calculations
- Astronomy: Measuring distances to stars
Common Triangle Measurements
| Measurement | Formula |
|---|---|
| Perimeter | P = a + b + c |
| Area (base-height) | A = ½ × base × height |
| Area (Heron’s formula) | A = √[s(s-a)(s-b)(s-c)] where s = ½P |
| Height (from side a) | hₐ = 2A/a |