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Triangle Calculator

Solve any triangle by entering 3 values.

Math
Triangle Calculator
Solve any triangle by entering 3 of its properties.

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A Comprehensive Triangle Solver

This powerful Triangle Calculator can solve for the missing angles and side lengths of any triangle, not just right-angled ones. By providing any three known properties (as long as at least one is a side), it will use trigonometric laws to find the remaining values.

The Formulas Explained

  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
    • Used when you know an angle and its opposite side (e.g., ASA, AAS cases).
  • Law of Cosines: c² = a² + b² - 2ab*cos(C)
    • Used when you know two sides and the angle between them (SAS case) or all three sides (SSS case).
  • Sum of Angles: A + B + C = 180°

How to Use the Calculator

  1. Enter Known Values: Input the three properties you know. For example, you might know two sides and the angle between them (Side A, Side B, Angle C).
  2. Leave Unknowns Blank: Leave the fields for the values you want to solve for empty.
  3. Calculate: The calculator will fill in the missing side lengths and angles.

Real-World Example

Given a triangle with Side a = 7, Side b = 10, and the angle between them, Angle C = 30° (SAS case).

  • Find Side c (Law of Cosines): c² = 7² + 10² - 2(7)(10)cos(30°) ≈ 27.75. So, c ≈ 5.27.
  • Find Angle A (Law of Sines): sin(A)/7 = sin(30°)/5.27. So, sin(A) ≈ 0.664, and A ≈ 41.6°.
  • Find Angle B (Sum of Angles): B = 180° - 30° - 41.6° ≈ 108.4°.

Frequently Asked Questions (FAQ)

  • What is the 'ambiguous case' (SSA)? When you know two sides and a non-included angle (Side-Side-Angle), there might be zero, one, or two possible triangles that fit the description. This simplified calculator may not handle all ambiguous cases correctly.
  • Why do I need to know at least one side? If you only know three angles (AAA), you know the shape of the triangle but not its size. There are infinitely many similar triangles with the same three angles. You need at least one side length to determine the scale.
  • Can I enter angles in radians? This calculator assumes all angle inputs are in degrees.