Scalene Triangle Solver
Angles: -
Heights: -
Medians: -
Area: -
Perimeter: -
Understanding Scalene Triangles
What is a Scalene Triangle?
A scalene triangle has all sides and angles of different lengths and measures. Key properties include:
- All sides have different lengths
- All angles have different measures
- No line of symmetry
- Three different heights
- Three different medians
- Three different angle bisectors
Key Formulas
Area Formulas
Heron's Formula: A = √(s(s-a)(s-b)(s-c))
where s = (a+b+c)/2
Height Formulas
h₁ = 2A/a
h₂ = 2A/b
h₃ = 2A/c
Median Formulas
m₁ = √(2(b²+c²) - a²)/2
Special Properties
Centroid
Divides each median in ratio 2:1
Orthocenter
Intersection of three altitudes
Circumcenter
Equidistant from all vertices
Incenter
Equidistant from all sides
Advanced Properties
Euler Line
Contains centroid, orthocenter, and circumcenter
Nine-Point Circle
Passes through midpoints of sides
Gergonne Point
Intersection of lines from vertices to opposite touchpoints
Nagel Point
Intersection of lines from vertices to opposite excircle touchpoints
Real-World Applications
Surveying
Used in land measurement and mapping
Engineering
Applied in structural analysis and design
Navigation
Essential in triangulation and GPS
Architecture
Used in complex geometric designs