Triangle Calculator
Calculate triangle area, perimeter, angles, and missing sides using multiple methods. Complete triangle solver for geometry.
Why Choose Our Triangle Calculator?
Designed by PhD mathematicians and validated against academic standards. Used by professors at leading universities.
Triangle Calculator
Calculate triangle area, perimeter, angles, and sides using various methods
Triangle Calculations
Length of the base
Perpendicular height to base
📐 Triangle Formulas
- • Area = ½ × base × height
- • Area = √[s(s-a)(s-b)(s-c)] (Heron's formula)
- • Area = ½ × a × b × sin(C)
- • Law of Cosines: c² = a² + b² - 2ab cos(C)
- • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Triangle Results
Area
Square units
Complete Triangle
Sides
Angles
Triangle Properties
- • Has a 90° angle - Pythagorean theorem applies
- • Sum of all angles = 180°
- • Any two sides must be greater than the third
🔢 Mathematical Applications
Mathematics provides powerful tools for solving problems and understanding patterns. This calculator helps you perform accurate calculations efficiently.
Best Practices
- • Verify input values
- • Check order of operations
- • Use appropriate precision
- • Validate results
Applications
- • Academic problems
- • Scientific research
- • Engineering design
- • Data analysis
Related Calculators
How to Use
- 1Enter your values in the input fields
- 2Review the calculated results
- 3Use the results for your planning
📚 Table of Contents
1Mastering Triangle Calculations
Calculate triangle area, perimeter, angles, and sides using various methods. Whether you're a student, educator, or professional, understanding the mathematical principles behind triangle will enhance your problem-solving abilities. This guide breaks down complex concepts into understandable components and provides practical applications for real-world scenarios.
Mathematical Foundations
The underlying mathematics involves fundamental principles that have wide-ranging applications. Understanding these concepts helps you: • Verify calculator results manually • Apply knowledge to related problems • Develop mathematical intuition • Solve more complex variations • Teach others effectively
Step-by-Step Problem Solving
Approach problems systematically: 1. Identify what you're solving for 2. Gather all necessary information 3. Choose the appropriate formula 4. Perform calculations carefully 5. Verify results make sense 6. Consider alternative methods
2Real-World Applications
Mathematical concepts aren't just theoretical - they have practical applications in many fields.
Professional Applications
Professionals in various fields use these calculations: • Engineers for design and analysis • Scientists for research and experiments • Financial analysts for modeling • Architects for planning and construction • Data scientists for analysis and predictions
Educational Value
For students and educators: • Builds foundational math skills • Develops logical thinking • Prepares for advanced topics • Provides exam preparation • Enables peer tutoring and collaboration
🔗 Related Resources
This comprehensive guide is regularly updated to ensure accuracy. Last reviewed: 9/8/2025
Frequently Asked Questions
How do I calculate the area of a triangle?
Common methods: 1) Base × Height ÷ 2 when you know base and height. 2) Heron's formula: √[s(s-a)(s-b)(s-c)] where s is semi-perimeter when you know all three sides. 3) (1/2)ab×sin(C) when you know two sides and included angle.
What are the different types of triangles?
By sides: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (no sides equal). By angles: Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°). Special: 30-60-90 and 45-45-90 triangles have fixed ratios.
How do I find a missing side or angle?
Use Law of Sines (a/sin(A) = b/sin(B) = c/sin(C)) when you know two angles and one side, or two sides and one opposite angle. Use Law of Cosines (c² = a² + b² - 2ab×cos(C)) when you know two sides and included angle, or all three sides.
What is the triangle inequality theorem?
The sum of any two sides must be greater than the third side. For sides a, b, c: a + b > c, a + c > b, and b + c > a. If this isn't satisfied, the three lengths cannot form a triangle. This calculator automatically checks this condition.
How do I calculate triangle height/altitude?
Height = 2 × Area ÷ Base. For any triangle with area A and base b, h = 2A/b. You can also use: h = a × sin(B) = b × sin(A) where a and b are sides and A and B are opposite angles. For equilateral triangles: h = (√3/2) × side.
What are common triangle formulas in construction and engineering?
Roof pitch: Rise/Run ratio forms right triangle. Truss calculations use triangle stability. Land surveying uses triangulation. Bridge design relies on triangular supports for strength. The 3-4-5 rule creates perfect right angles on construction sites.