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Pythagoras and trigonometry

IGCSE Mathematics 0580, topics 6.1 and 6.2. Pythagoras' theorem with a proof, sine, cosine and tangent in right-angled triangles, elevation and depression, bearings and the shortest distance to a line.

About this lab: Pythagoras and trigonometry

Interactive simulation for Cambridge IGCSE Mathematics 0580 topics 6.1 and 6.2: squares on the sides of a right-angled triangle and a proof of Pythagoras' theorem by rearranging, finding the hypotenuse or a shorter side and testing for a right angle, SOH CAH TOA with opposite and adjacent sides that swap with the angle, step-by-step solving of right-angled triangles, angles of elevation and depression, bearings split into east and north parts, and the shortest distance from a point to a line.

IGCSE Mathematics 0580, topics 6.1 and 6.2. Pythagoras' theorem with a proof, sine, cosine and tangent in right-angled triangles, elevation and depression, bearings and the shortest distance to a line.

Pythagoras and trigonometry is a free, browser-based simulation for Cambridge IGCSE Mathematics 0580 (topic 6 Trigonometry, sections 6.1 Pythagoras' theorem, 6.2 Right-angled triangles). The course is assessed in Paper 1 (Core non-calculator), Paper 2 (Extended non-calculator), Paper 3 (Core calculator), Paper 4 (Extended calculator). Syllabus for examination in 2025-2027. There are 7 tabs, each a self-contained experiment with its own controls and live readings, and nothing to install: it runs on a laptop, tablet or classroom projector.

Syllabus coverage

Full syllabus map: IGCSE Mathematics 0580 topic 6.

How to use this simulation

  1. 1. Pythagoras' theorem.
  2. 2. Using Pythagoras.
  3. 3. SOH CAH TOA.
  4. 4. Solve the triangle.
  5. 5. Elevation and depression.
  6. 6. Bearings.
  7. 7. Shortest distance.
  8. The buttons at the end of the tab strip give the scene the whole window (Full screen, Hide controls) and, on a dark stage, a projector-friendly palette (Light scene). Many scenes also have drag handles: drag them to change the set-up directly.

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