Triangle Calculator

Triangle Solving Methods:

Given sufficient information (any of these combinations):

Three sides (SSS)
Two sides and included angle (SAS)
Two angles and one side (ASA or AAS)
Right triangle: two sides or one side and one angle

Side a:

units

Side b:

units

Side c:

units

Angle A:

degrees

Angle B:

degrees

Angle C:

degrees

Results:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Triangle Calculator?

The Triangle Calculator solves for unknown sides and angles of a triangle when given sufficient information. It can handle various combinations of known values including sides (SSS), angles and sides (ASA, AAS, SSA), or two sides and the included angle (SAS).

2. How Does the Calculator Work?

The calculator uses trigonometric principles including:

Law of Cosines:

\[ c^2 = a^2 + b^2 - 2ab\cos(C) \]

Law of Sines:

\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \]

Angle Sum Property:

\[ A + B + C = 180° \]

3. Triangle Solving Methods

Different cases:

SSS (Side-Side-Side): When all three sides are known, use Law of Cosines to find angles
SAS (Side-Angle-Side): When two sides and the included angle are known, use Law of Cosines to find the third side
ASA (Angle-Side-Angle): When two angles and the included side are known, use Angle Sum Property then Law of Sines
AAS (Angle-Angle-Side): When two angles and a non-included side are known, similar to ASA
SSA (Side-Side-Angle): The ambiguous case - may have 0, 1, or 2 solutions

4. Using the Calculator

Instructions: Enter any 3 elements of the triangle (sides and/or angles). The calculator will solve for the remaining elements. Sides must be positive numbers. Angles must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What if I get an error message?
A: This usually means the values you entered don't form a valid triangle. Check that angles sum to 180° and sides satisfy the triangle inequality theorem.

Q2: Why does my SSA case have two solutions?