Triangle Calculator
Solve triangles given sides and angles. Calculate area, perimeter, and other properties.
Enter Known Values
Enter at least 3 values (SSS, SAS, ASA, AAS). Sides a, b, c are opposite to angles A, B, C.
Sides
Angles (degrees)
Formulas Used
- • Law of Cosines: c² = a² + b² - 2ab·cos(C)
- • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- • Area (Heron's): √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2
- • Inradius: Area / s
- • Circumradius: abc / (4·Area)
Puzzle Tips
- • Triangulation is common in multi-cache puzzles
- • Area or angle calculations may give coordinate digits
- • Right triangles have special properties (a² + b² = c²)
- • Equilateral triangles have all 60° angles
Triangle Calculator
This tool solves triangles given various combinations of sides and angles. Enter at least three values to calculate all properties of the triangle.
Solving Methods
SSS (Side-Side-Side)
All three sides known. Uses Law of Cosines to find angles.
SAS (Side-Angle-Side)
Two sides and the included angle. Uses Law of Cosines for third side.
ASA (Angle-Side-Angle)
Two angles and the included side. Uses Law of Sines.
AAS (Angle-Angle-Side)
Two angles and a non-included side. Third angle = 180° - A - B.
Properties Calculated
- Area: Using Heron's formula
- Perimeter: Sum of all sides
- Inradius: Radius of inscribed circle
- Circumradius: Radius of circumscribed circle
- Type: Acute/Right/Obtuse, Scalene/Isosceles/Equilateral
In Geocaching
Triangle calculations are useful for:
- Triangulation: Finding position from multiple points
- Area puzzles: Calculating land areas
- Bearing problems: Navigation calculations
- Survey markers: Understanding historical surveys
Important Formulas
- Law of Cosines: c² = a² + b² - 2ab·cos(C)
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- Pythagorean: a² + b² = c² (right triangles only)