Altitude of Triangle Calculator
Choose one of the three methods below to find the altitude (height) of a triangle.
About the Altitude of Triangle Calculator
The Altitude of Triangle Calculator is a scientifically accurate tool that computes the height (altitude) from any vertex to the opposite side using three proven methods: direct base+height, Heron’s formula (SSS), and trigonometry (SAS). This Altitude of Triangle Calculator delivers precise results trusted by students, engineers, architects, and researchers worldwide. Proudly supported by Agri Care Hub.
Scientific Formulas Used
Method 2 (SSS): Area = √[s(s−a)(s−b)(s−c)] → h = 2×Area / base (Heron’s formula)
Method 3 (SAS): Area = ½ × side₁ × side₂ × sin(angle) → h = 2×Area / base
Why the Altitude of Triangle Calculator Is Important
The altitude is one of the most fundamental measurements in geometry. It is required to calculate area, volume of prisms/pyramids, structural load in engineering, land surveying, roofing, agriculture field planning, and countless real-world applications. Knowing the exact height of a triangle — even when only sides are known — is essential in construction, computer graphics, robotics, and physics simulations.
How to Use the Altitude of Triangle Calculator
- Choose the method you have data for.
- Enter the known values (leave others blank).
- Click “Calculate Altitude”.
- Get instant, accurate results with full step-by-step explanation.
When Should You Use This Calculator?
- Geometry homework & exams
- Engineering & architectural drawings
- Land surveying and agriculture (field area calculation)
- Roofing and construction (rafter length, material estimation)
- Computer graphics and 3D modeling
- Physics problems involving forces and equilibrium
Scientific Foundation
Heron’s formula dates back to around 60 AD and has been rigorously proven in Euclidean geometry. The trigonometric area formula (½ab sin C) was established by Euclid and remains exact. All calculations use double-precision arithmetic for maximum accuracy. Full mathematical treatment available at Wikipedia: Altitude of Triangle.
Real-World Examples
• A plot with sides 30m, 40m, 50m has altitude to the 50m base = 24m (Heron’s formula).
• A roof triangle with two sides 5m and included angle 40° has height ≈ 3.21m.
• Surveyors use altitude calculations daily to compute land area from measured boundaries.
Conclusion
The Altitude of Triangle Calculator puts centuries of geometric knowledge at your fingertips. Whether you’re a student, engineer, farmer, or architect, this tool delivers mathematically perfect results instantly. For more precision tools, visit Agri Care Hub.
