Triangle Height Calculator

Category: Geometry
- April 18, 2025
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Calculate the height of a triangle using different methods. The height (altitude) is the perpendicular distance from a vertex to the opposite side.

Select Calculation Method

units
sq. units

Display Options

About Triangle Heights

The height (or altitude) of a triangle is the perpendicular distance from a vertex to the line containing the opposite side. A triangle has three heights, one from each vertex to the opposite side.

Methods for Calculating Triangle Height
  • Base and Area: If you know the base (b) and area (A) of a triangle, the height (h) is calculated using h = 2A/b.
  • Three Sides (Hero's Formula): If you know all three sides of a triangle, you can calculate the height using Hero's formula for the area and then solve for the height.
  • Two Sides and Angle: If you know two sides and the angle between them, you can calculate the height using trigonometry.
  • Coordinates: If you know the coordinates of all three vertices, you can calculate the height using coordinate geometry.
Applications of Triangle Heights
  • Engineering: Used in structural analysis, bridge design, and architectural planning
  • Surveying: Calculating land areas and distances
  • Physics: Center of mass and moment of inertia calculations
  • Computer Graphics: Rendering and collision detection algorithms
  • Navigation: Distance calculations and route planning

Triangle Height Calculator – A Practical Guide

Common Formulas Used:

  • Height from Area and Base: 

    \( h = \frac{2A}{b} \)

  • Height from Three Sides: 

    \( h = \frac{2 \times \sqrt{s(s-a)(s-b)(s-c)}}{side} \)

  • Height from Two Sides and an Angle: 

    \( h = side \times \sin(\theta) \)

  • Height from Coordinates: 

    \( h = \frac{2 \times \text{Area}}{\text{Base Length}} \)

What Does the Triangle Height Calculator Do?

The Triangle Height Calculator is a triangle geometry solver that helps you calculate the height (also known as the altitude) of a triangle using different methods. The height is the perpendicular distance from a vertex to the line opposite it. This tool is especially useful when you need to calculate triangle dimensions, whether you're working with side lengths, angles, area, or coordinates.

Why Use This Calculator?

Heights are essential in understanding and solving triangle properties. Whether you're a student, teacher, engineer, or builder, this calculator can quickly compute accurate results using several geometric formulas. It also acts as a triangle side and angle tool, making it more than just a basic triangle solver.

How to Use the Calculator

Select a method depending on the data you have available. The calculator supports the following:

  • Base and Area: Enter the base length and the area of the triangle.
  • Three Sides: Use this method if you know all side lengths. It applies Hero’s Formula to calculate the height.
  • Two Sides and an Angle: Use when you know two sides and the angle between them.
  • Coordinates: Input the (x, y) values for all three triangle points.

After inputting the necessary values, click “Calculate Height”. You can also choose how many decimal places to display and whether to show step-by-step calculations.

Key Features

  • Supports multiple triangle solving methods
  • Visual diagram of the triangle and its height
  • Calculation steps for better understanding
  • Adjustable precision and display options

Who Can Benefit From This Tool?

This Triangle Height Calculator is ideal for:

  • Students studying geometry or trigonometry
  • Teachers creating examples or checking solutions
  • Architects and engineers needing fast, reliable calculations
  • Anyone working with triangles in design, layout, or graphics

FAQs

Can this tool calculate other triangle measurements?
Yes, it also shows area, perimeter, and other related values depending on the selected method.

Is this the same as a Pythagorean Theorem tool?
No, but the calculator uses related principles when working with right triangles. If you want to specifically calculate hypotenuses or side lengths, a Pythagorean theorem tool or right triangle calculator would be a better choice.

Can I use coordinates to find the height?
Yes, the coordinate method uses geometry to calculate the area first and then finds the perpendicular height from a chosen vertex.

Related Tools and Concepts

This tool complements other useful calculators like the Triangle Area Calculator, Right Triangle Solver, and Distance Calculator. These help calculate triangle side lengths, find triangle angles, or measure distance between points—making it part of a full triangle geometry helper set.

Summary

Whether you're working with side lengths, angles, or coordinates, the Triangle Height Calculator makes it easy to solve triangle measurements. It’s a reliable triangle geometry solver for practical, everyday use in math, design, and engineering.