Oblique Triangle Calculator
Solve any oblique triangle using SSS, SAS, ASA, or AAS methods
Calculate Oblique Triangle
Example Calculation
SSS Example
Given: Sides a = 5, b = 7, c = 9
Method: Use Law of Cosines to find angles
Formula: cos(C) = (a² + b² - c²) / (2ab)
Result: Angles ≈ 33.6°, 46.6°, 99.8°
SAS Example
Given: Sides a = 4, b = 5, Angle C = 40°
Method: Use Law of Cosines for third side, Law of Sines for angles
Area Formula: A = ½ab sin(C)
Result: Area ≈ 6.428 square units
Key Formulas
Law of Cosines
c² = a² + b² - 2ab cos(C)
Used when you know two sides and included angle (SAS) or three sides (SSS)
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Used for ASA and AAS problems
Area Formula
A = ½ab sin(C)
Heron's formula for SSS cases
Triangle Types
Acute Triangle
All angles < 90°
Right Triangle
One angle = 90°
Obtuse Triangle
One angle > 90°
Understanding Oblique Triangles
What is an Oblique Triangle?
An oblique triangle is any triangle that doesn't contain a right angle (90°). This includes acute triangles (all angles less than 90°) and obtuse triangles (one angle greater than 90°).
Solution Methods
- •SSS: Three sides known - use Law of Cosines
- •SAS: Two sides and included angle - use Law of Cosines
- •ASA: Two angles and included side - use Law of Sines
- •AAS: Two angles and non-included side - use Law of Sines
Key Properties
- ✓Sum of interior angles always equals 180°
- ✓Triangle inequality: sum of any two sides > third side
- ✓Largest angle opposite to longest side
- ✓Can be solved using trigonometric laws
Note: SSA (two sides and non-included angle) can be ambiguous and may have 0, 1, or 2 solutions.