Triangle Solver Online | Triangle Calculator Tool
Free online triangle solver and triangle calculator for solving triangles using various methods including SSS, SAS, ASA, and AAS. This comprehensive trigonometry calculator helps students, engineers, and mathematicians find missing angles, sides, area, perimeter, and other triangle properties with step-by-step solutions for educational and professional applications.
Solution Method
Enter Triangle Measurements
Side a:
Side b:
Side c:
Formulas Used:
Law of Cosines: cos(A) = (b² + c² - a²) / (2bc)
Typical Use Cases
Our triangle solver online serves students, engineers, and surveyors working with triangular calculations. Mathematics students use this triangle calculator for homework verification, learning trigonometry concepts, and solving complex triangle problems using SSS, SAS, ASA, and AAS methods with detailed mathematical solutions.
Engineering professionals rely on this trigonometry calculator for structural analysis, surveying applications, and mechanical design calculations. Architects use this geometric calculator for roof design, triangular framework analysis, and construction planning requiring precise triangle property computations.
Triangle Solution Methods
SSS (Side-Side-Side):
When you know all three sides of a triangle.
SAS (Side-Angle-Side):
When you know two sides and the included angle.
ASA (Angle-Side-Angle):
When you know two angles and the included side.
AAS (Angle-Angle-Side):
When you know two angles and a non-included side.
SSA (Side-Side-Angle):
When you know two sides and a non-included angle (may have 0, 1, or 2 solutions).
Key Triangle Formulas
Area Formulas:
- Base × Height ÷ 2
- ½ × ab × sin(C) (two sides and included angle)
- Heron's Formula: √s(s-a)(s-b)(s-c) where s = (a+b+c)/2
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines:
c² = a² + b² - 2ab×cos(C)
Applications of Triangle Calculations
Science & Engineering
- Structural analysis in civil engineering
- Force vector calculations in physics
- Navigation and GPS triangulation
- Optics and light ray paths
Architecture & Design
- Roof truss design
- Land surveying
- Computer graphics and 3D modeling
- Pattern design and geometric art
Types of Triangles
Triangles can be classified based on their sides and angles:
By Sides
Equilateral:
All three sides are equal in length.
Isosceles:
Two sides are equal in length.
Scalene:
All three sides have different lengths.
By Angles
Acute:
All angles are less than 90°.
Right:
One angle is exactly 90°.
Obtuse:
One angle is greater than 90°.
Special Triangles
30-60-90 Triangle:
Right triangle with these three angles.
45-45-90 Triangle:
Isosceles right triangle.