Triangle Calculator

Length of the base
Must be a positive number
Length of the height
Must be a positive number
Length of the hypotenuse

Triangle Properties

6.00
Area
12.00
Perimeter
Right
Triangle Type
90°, 53.13°, 36.87°
Angles

Interpretation

This is a right triangle with sides of length 3, 4, and 5. The area is 6 square units, and the perimeter is 12 units. The angles are 90°, 53.13°, and 36.87°. This triangle follows the Pythagorean theorem (3² + 4² = 5²).

Calculation Steps

Using the Pythagorean theorem: c² = a² + b²
Side A = 3, Side B = 4
Hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5
Area = (1/2) × base × height = (1/2) × 3 × 4 = 6
Perimeter = 3 + 4 + 5 = 12
Angle A = arctan(4/3) ≈ 53.13°
Angle B = 90° - 53.13° = 36.87°

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Triangle Calculator Guide

What is a Triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. Triangles are classified based on their side lengths and angles, and they have unique properties that make them fundamental in mathematics, engineering, architecture, and many other fields.

Our triangle calculator helps you solve for various triangle properties including side lengths, angles, area, and perimeter. Whether you're working with a right triangle, equilateral triangle, or any other type, this tool provides accurate calculations with detailed explanations.

Types of Triangles

Right Triangle
Has one 90° angle. Follows the Pythagorean theorem: a² + b² = c²
Equilateral Triangle
All three sides are equal. All angles are 60°.
Isosceles Triangle
Two sides are equal. Two angles are equal.
Scalene Triangle
All sides are different. All angles are different.

Key Triangle Formulas

Our calculator uses standard geometric formulas to ensure accurate results:

Pythagorean Theorem (Right Triangles)

a² + b² = c²

Where a and b are the legs, and c is the hypotenuse of a right triangle.

Area of a Triangle

Area = (1/2) × base × height

For any triangle, the area is half the product of its base and height.

Heron's Formula (SSS Triangles)

s = (a + b + c) / 2
Area = √[s(s - a)(s - b)(s - c)]

Where a, b, c are the side lengths, and s is the semi-perimeter.

Law of Cosines (SAS Triangles)

c² = a² + b² - 2ab cos(C)

Where a and b are two sides, C is the included angle, and c is the third side.

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C) = 2R

Where a, b, c are sides, A, B, C are opposite angles, and R is the circumradius.

How to Use This Triangle Calculator

Using our triangle calculator is straightforward:

  1. Select triangle type - Choose from right, equilateral, isosceles, scalene, SSS, or SAS
  2. Enter known values - Input the side lengths and/or angles you know
  3. Calculate - Click the calculate button to compute all triangle properties
  4. Review results - Examine the calculated values, visualization, interpretation, and calculation steps

The calculator automatically validates your inputs and provides helpful error messages if needed. It also offers detailed step-by-step explanations to help you understand how each property was calculated.

Practical Applications

Triangle calculations have numerous practical applications across various fields:

Architecture and Construction: Calculating roof pitches, determining structural angles, and planning building layouts.

Engineering: Designing mechanical components, calculating forces in trusses, and analyzing structural stability.

Navigation and Surveying: Determining distances using triangulation, calculating elevations, and mapping terrain.

Computer Graphics: Rendering 3D models, calculating surface normals, and implementing collision detection.

Physics: Analyzing vector components, calculating trajectories, and solving force diagrams.

Education: Teaching geometry concepts, solving textbook problems, and verifying homework solutions.

triangle calculator right triangle pythagorean theorem triangle area triangle perimeter geometry calculator triangle angles heron's formula law of sines law of cosines

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