IA ideas library
Trigonometry IA ideas: navigation, surveying and measuring the unreachable
Trigonometry was invented to measure things you can't reach: the height of a cliff, the width of a river, the distance to a ship. These ideas put the sine and cosine rules, bearings and 3D trigonometry to work on real measurements you take yourself.
The mathematics is in both SL courses, which makes these good first IAs. Reach the higher bands by measuring the same thing several ways, propagating your measurement error through the formula, and deciding which method you would trust.
Trigonometry, navigation & surveying ideas (8)
- How wide is the river? Measuring a distance you can't crossAA SLAI SLAccessible
- How far can you see from the top of a hill?AA SLAI SLAA HLSolid
- How far off do you end up? Navigating a route by bearingsAA SLAI SLAccessible
- What is the best angle to sail upwind?AA HLAA SLAI HLAmbitious
- Measuring the area of an irregular field with trianglesAA SLAI SLAccessible
- Measuring the Earth with a stick and a partner schoolAA SLAI SLAA HLSolid
- Designing an accessible ramp for a real entranceAA SLAI SLAccessible
- The hidden angles of a hip roof: 3D trigonometryAA SLAI SLAA HLSolid
Also relevant (9)
- Which method measures a building's height most accurately?AA SLAI SLAccessible
- Designing a working sundial for my latitudeAA SLAA HLAI SLAI HLSolid
- Why do flight paths curve on the map?AA SLAA HLAI SLAI HLAmbitious
- Modelling the sun's height from a stick's shadowAA SLAI SLAA HLAI HLAccessible
- Why do two nearly-equal notes 'wobble'? Beats and trigonometric identitiesAA SLAA HLAI SLAI HLSolid
- Animating a logo with transformation matricesAI HLAA HLSolid
- How does a game draw 3D on a flat screen? Projection matricesAI HLAA HLAmbitious
- Why is a rolling marble slower than a sliding block?AA SLAI SLAA HLSolid
- Crossing a river with a current: fastest or straightest?AA HLAI HLAA SLSolid
Frequently asked questions
Is a trigonometry IA too simple?
Not if it goes beyond one calculation. Comparing methods, analysing how errors in angles and lengths affect the answer, and checking against an independent measurement make it a full exploration.
What equipment do I need?
A tape measure and a clinometer (a phone app or a protractor with a weighted string) are enough for most of these ideas. A free map with a scale helps for larger distances.
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Related types of IA: Geometry, trigonometry & Voronoi diagrams
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