What is the Triangle Solver & Visualizer?
Quick Answer: Enter any three known parts of a triangle (sides and/or angles) and instantly compute all missing sides, angles, area, perimeter, and draw the triangle with circumcircle and incircle. Supports SSS, SAS, ASA, AAS configurations.
Theory of Triangle Solving
A triangle is determined by three independent measurements. The tool uses the Law of Cosines (c² = a² + b² - 2ab cos C) and the Law of Sines (a/sin A = b/sin B = c/sin C) to find unknown sides and angles. The area is computed via Heron's formula or ½ ab sin C. The circumradius R = abc / (4 * area) and inradius r = area / s, where s is the semiperimeter. The triangle is drawn to scale with vertices placed using coordinate geometry.
Step-by-Step Examples
Example 1: SSS Triangle
- Select SSS, enter sides a=3, b=4, c=5.
- Click Solve. The right triangle appears with angles 36.87°, 53.13°, 90°.
- Circumcircle (through all vertices) and incircle (touching all sides) are drawn automatically.
Example 2: SAS Configuration
- Choose SAS, enter side a=5, angle C=60°, side b=7.
- The tool computes side c and the remaining angles using the law of cosines.
- Observe how the included angle shapes the triangle.
Frequently Asked Questions
What input combinations are accepted?
SSS (3 sides), SAS (2 sides and included angle), ASA (2 angles and included side), AAS (2 angles and a non-included side). All angles must be in degrees.
What if my inputs do not form a valid triangle?
The tool checks triangle inequality and angle sum. An error message will appear if the triangle is impossible.
How accurate are the drawn circumcircle and incircle?
They are computed exactly from the solved triangle's coordinates, so the circles will touch vertices or sides precisely.
Can I see the side lengths on the drawing?
Yes, when Labels is checked, side lengths and angle values are displayed next to the corresponding edges/vertices.
Is the triangle drawn to scale?
Yes, the drawing is scaled to fit the canvas while preserving proportions. Zoom and pan are not available; use Reset View to re-center.