Triangle Sides Calculator
Find missing sides using various methods
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Methods for Finding Triangle Sides
There are several methods to find missing sides of a triangle, depending on what information you have available.
Law of Cosines (SAS)
When you know two sides and the included angle, use the law of cosines:
c² = a² + b² - 2ab·cos(C)
Law of Sines (ASA or AAS)
When you know two angles and a side, use the law of sines:
a/sin(A) = b/sin(B) = c/sin(C)
Pythagorean Theorem (Right Triangles)
For right triangles with one 90° angle:
a² + b² = c² (where c is the hypotenuse)
Frequently Asked Questions
What is the law of cosines?
The law of cosines relates the sides and angles: c² = a² + b² - 2ab·cos(C). It's used when you know two sides and the included angle.
What is the law of sines?
The law of sines states that a/sin(A) = b/sin(B) = c/sin(C). It's used when you know two angles and a side.
What information do I need to find a side?
You need at least two sides and an angle (SAS or SSA), or two angles and a side (ASA or AAS) to calculate missing sides.
Can I find sides with only angles?
No, you need at least one side length. Angles alone determine the shape but not the size of the triangle.
What is the SSA ambiguous case?
When you know two sides and a non-included angle, there may be 0, 1, or 2 possible triangles that satisfy the conditions.
Which method should I use?
Use law of cosines for SAS, law of sines for ASA/AAS, and Pythagorean theorem for right triangles.