Triangle calculator SSA

The calculator solves the triangle given by two sides and a non-included angle between them (abbreviation SSA side-side-angle). The SSA (Side-Side-Angle) theorem is a statement in geometry that states that if two sides of a triangle have a given ratio to two sides of another triangle and the included angle between those sides is the same in both triangles, then the triangles are congruent. It's important to note that this theorem doesn't guarantee congruence in all cases, it is only a necessary but not sufficient condition.

To calculate the missing information of a triangle when given the SSA theorem, you can use the known side lengths and angles to find the remaining side length and angles using trigonometry or geometry.

If you know the ratio of two sides (a/b) and the measure of the angle (C) between them, you can use the Law of Cosines to find the length of the third side (c) as:

c² = a² + b² - 2ab * cos(C)

Once you have the length of the third side, you can use the Law of Sines to find the remaining angles (A and B) as:

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

Where R is the circumradius of the triangle

It's important to note that the SSA Theorem can be used only if the included angle between the two sides is obtuse, otherwise it may not provide a unique solution, and it's not always possible to determine the triangle completely.

Look also at our friend's collection of math problems and questions:

• triangle
• right triangle
• Heron's formula
• The Law of Sines
• The Law of Cosines
• Pythagorean theorem
• triangle inequality
• similarity of triangles
• The right triangle altitude theorem

See triangle basics on Wikipedia or more details on solving triangles.