30 60 90 and 45 45 90 right triangle calculator

What is this length?
30 60 90 triangle> or or

45 45 90 triangle> or


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What is a 30-60-90 and 45-45-90 Right Triangle Calculator?

A 30-60-90 and 45-45-90 Right Triangle Calculator is a tool used to calculate the missing sides and angles of these special right triangles based on their known properties.

Special Right Triangles:

  1. 30-60-90 Triangle:

    • The angles are 30°, 60°, and 90°.
    • The sides follow the ratio: 1:√3:2 (short leg : long leg : hypotenuse)
    • If you know one side, you can calculate the others using this ratio.

  2. 45-45-90 Triangle:

    • The angles are 45°, 45°, and 90°.
    • The sides follow the ratio: 1:1:√2 ​ (leg : leg : hypotenuse)
    • Since both legs are equal, you can find any missing side using this ratio.

Why Use a 30-60-90 and 45-45-90 Triangle Calculator?

✅ Saves Time – No need to manually apply ratios or the Pythagorean Theorem.
✅ Eliminates Errors – Ensures accurate calculations.
✅ Useful in Geometry and Trigonometry – Helps in solving problems quickly.
✅ Practical for Engineering and Physics – Common in construction, design, and physics applications.

How Does the Calculator Work?

  1. Input:
    • Select the triangle type (30-60-90 or 45-45-90).
    • Enter a known value (e.g., leg length, hypotenuse).
  2. Computation:
    • Uses special triangle ratios to calculate missing sides.
  3. Output:
    • Displays the unknown side lengths and angles.

When is This Calculator Used?

  • In Geometry: Solving problems involving right triangles.
  • In Trigonometry: Finding sine, cosine, and tangent values.
  • In Physics & Engineering: Designing structures, ramps, or components.
  • In Real Life: Roof construction, ramps, and other triangular designs.