What quantity did you change?
Labs / Mathematics
Triangle Solver
Grab corners A, B, and C and reshape the triangle any way you like — every side length, interior angle, and the area update as you move. Switch to SSS, SAS, or ASA to build a triangle from just a few given parts, and see which law — Sines or Cosines — unlocks the rest.
Labs / Mathematics / Triangle Solver
Triangle Solver
Grab corners A, B, and C and reshape the triangle any way you like — every side length, interior angle, and the area update as you move. Switch to SSS, SAS, or ASA to build a triangle from just a few given parts, and see which law — Sines or Cosines — unlocks the rest.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
a —b —c —A —B —C —area —solves —
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Do the three angles always add up to the same total, no matter how you drag the corners?
- Lock ∠C to 90° and drag a corner — how do a, b, and c relate now? Does a² + b² look familiar?
- In SAS, widen the given angle A while keeping the two sides fixed. Which way does the opposite side a grow, and how fast?
- In SSS, why do some slider combinations refuse to make a triangle at all?
- Turn on the circumcircle: as you reshape the triangle, is each side's length divided by the sine of its opposite angle really the same value?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.