Triangle Side Calculator
Calculate missing triangle sides using perimeter, Law of Cosines, or Law of Sines
Calculate Triangle Sides
Results - Two Sides + Perimeter
Example Calculations
Example 1: Two Sides + Perimeter
Given: Side A = 5, Side B = 7, Perimeter = 18
Solution: Side C = P - (A + B) = 18 - (5 + 7) = 6
Result: Triangle with sides 5, 7, and 6 units
Example 2: Two Sides + Included Angle
Given: Side A = 8, Side B = 6, Angle C = 60°
Law of Cosines: c² = a² + b² - 2ab cos(C)
Solution: c² = 8² + 6² - 2(8)(6)cos(60°) = 64 + 36 - 48 = 52
Result: Side C = √52 ≈ 7.21 units
Example 3: Two Angles + One Side
Given: Angle A = 45°, Angle B = 60°, Side C = 10
Third Angle: C = 180° - 45° - 60° = 75°
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Result: Side A ≈ 7.32, Side B ≈ 8.97, Side C = 10
Triangle Properties
Sum of Angles
All interior angles sum to 180°
Triangle Inequality
Sum of any two sides > third side
Perimeter
Sum of all three sides
Calculation Tips
Use Law of Cosines when you know two sides and included angle
Use Law of Sines when you know two angles and one side
Check triangle inequality: a + b > c for all side combinations
Verify all angles sum to 180 degrees
Understanding Triangle Side Calculations
Methods for Finding Missing Sides
1. Two Sides + Perimeter
The simplest method when you know two sides and the total perimeter.
c = P - (a + b)
2. Law of Cosines
Used when you know two sides and the included angle between them.
c² = a² + b² - 2ab cos(C)
3. Law of Sines
Applied when you know two angles and one side (AAS or ASA cases).
a/sin(A) = b/sin(B) = c/sin(C)
Triangle Validation
Triangle Inequality
For any triangle with sides a, b, and c, the following must be true:
- • a + b > c
- • a + c > b
- • b + c > a
Angle Sum Property
The sum of all interior angles in any triangle equals 180°.
A + B + C = 180°
Applications
- • Construction and engineering
- • Navigation and surveying
- • Computer graphics
- • Physics and astronomy