45-45-90 Triangle Calculator | Special Right Triangle | CalcDeck

45-45-90 Triangle Calculator

a a a√2 90° 45° 45°
Days Until Days Until December 9 Days Until Days Until September 9 Convert From Millisiemens Calendar July 2022

Understanding the 45-45-90 Triangle

A 45-45-90 triangle is a special right triangle with unique properties that make it valuable in geometry and real-world applications. It has two 45-degree angles and one 90-degree angle, making it both a right triangle and an isosceles triangle.

Key Properties

In a 45-45-90 triangle:

  • The two legs are equal in length (marked as 'a')
  • The hypotenuse is equal to a√2 (where 'a' is the length of a leg)
  • The area is calculated as a²/2
  • The perimeter is a(2 + √2)

Common Applications

45-45-90 triangles are frequently used in:

  • Architecture and construction for creating perfect corners
  • Engineering design for symmetric structures
  • Computer graphics for diagonal measurements
  • Navigation and surveying