Triangle Degree Calculator
Calculate triangle angles using various methods: three sides, two angles, or angle with two sides
Calculate Triangle Angles
Choose the information you have about your triangle
Triangle Angles
Enter the required values to calculate triangle angles
Example: Equilateral Triangle
Given Information
Three sides: a = 5 cm, b = 5 cm, c = 5 cm
Method: Law of Cosines
Solution
α = arccos[(5² + 5² - 5²) / (2 × 5 × 5)] = arccos[25/50] = arccos[0.5] = 60°
β = arccos[(5² + 5² - 5²) / (2 × 5 × 5)] = 60°
γ = 180° - 60° - 60° = 60°
Result: All angles are 60° (Equilateral Triangle)
Triangle Types by Angles
Acute Triangle
All angles less than 90°
Right Triangle
One angle equals exactly 90°
Obtuse Triangle
One angle greater than 90°
Triangle Properties
Sum of all angles equals 180°
Largest angle is opposite the longest side
Smallest angle is opposite the shortest side
Triangle inequality: sum of any two sides > third side
Understanding Triangle Angle Calculations
Methods for Finding Angles
Three Sides (SSS)
Use the Law of Cosines to find all angles when you know all three side lengths.
α = arccos[(b² + c² - a²) / (2bc)]
Two Angles
Use the angle sum property: the sum of all angles in a triangle equals 180°.
Missing angle = 180° - (angle1 + angle2)
One Angle + Two Sides
Combine Law of Sines and Law of Cosines to find all angles.
First find the third side, then calculate all angles
Key Formulas
Angle Sum Property
α + β + γ = 180°
Law of Cosines
c² = a² + b² - 2ab·cos(γ)
γ = arccos[(a² + b² - c²) / (2ab)]
Law of Sines
a/sin(α) = b/sin(β) = c/sin(γ)
Note: All angle measurements are in degrees. The triangle inequality must be satisfied for valid triangles.