IA idea · Geometry, trigonometry & Voronoi diagrams
Which method measures a building's height most accurately?
Research question
Of a clinometer, the shadow method and a phone's barometer, which gives the most accurate and precise height for [a building of known height], and how does the error depend on distance?
Make it yours, then agree it with your teacher.
Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
Why it makes a good exploration
Trigonometry is taught with neat triangles, but real measurements have error. Comparing three methods on a building whose height is published lets you quantify which method works best and why.
The mathematics you'll need
- Right-angled trigonometry
- Similar triangles (shadows)
- Barometric pressure–height relationship (explain)
- Error propagation: how an angle error affects height
- Mean, standard deviation and percentage error
Where the data comes from
Measure a building of published height at several distances with a clinometer app, its shadow, and phyphox's barometer on stairs or a lift.
- phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.
A possible outline
- Describe the three methods and their assumptions.
- Collect repeated measurements.
- Compute heights and compare accuracy and precision.
- Model how angle error affects height at different distances; find the best distance.
- Reflect on which method you would trust and why.
Pitfalls that cost marks
- Forgetting eye height.
- Measuring shadows at different times.
- No repeated measurements.
Showing personal engagement
- Choose a building you know.
- Predict the best distance before measuring.
- Test your optimal-distance prediction.
See Criterion C: personal engagement for what examiners look for.
Which course is it for?
| Course | Fit | Maths to lean on |
|---|---|---|
| AA SL | Good fit | Right-angled trigonometry; Similar triangles (shadows) |
| AA HL | Not a natural fit | The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E. |
| AI SL | Good fit | Right-angled trigonometry; Similar triangles (shadows) |
| AI HL | Not a natural fit | The mathematics is mainly from the AA course; an AI HL version would need modelling with technology, statistics or networks at HL level. |
Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.
How this idea reaches the top bands
Reflection (D)
For this idea, start with the weak points: forgetting eye height; and measuring shadows at different times. Say how each one affects your answer.
Use of mathematics (E)
SL: right-angled trigonometry; similar triangles (shadows); barometric pressure–height relationship (explain); error propagation: how an angle error affects height; mean, standard deviation and percentage error, each explained in your own words and carried out correctly.
How geometry & voronoi explorations reach the top bands in general: Geometry, trigonometry & Voronoi diagrams IA ideas. Guides: A · B · C · D · E · self-grade sheet.
Taking it further
Use calculus to find the distance that minimises the height error for a given angle error.
Extending it for HL
Add an HL technique the question genuinely needs: what an HL geometry & voronoi exploration adds.
See a complete IA, marked
When is the sea warm enough for our swimming club? A sinusoidal model of sea temperature (AI SL) is a complete geometry & voronoi exploration, marked on every criterion.
Frequently asked questions
Which IB Maths course is this IA idea for?
It works for AA SL and AI SL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.
What mathematics does this IA use?
Right-angled trigonometry, similar triangles (shadows), barometric pressure–height relationship (explain), error propagation: how an angle error affects height and mean, standard deviation and percentage error.
Where can I get data for this IA?
Measure a building of published height at several distances with a clinometer app, its shadow, and phyphox's barometer on stairs or a lift. Checked sources and tools: phyphox (RWTH Aachen).
Turn this idea into your IA
The planner opens with “Which method measures a building's height most accurately?” filled in: the question, the maths and the data sources.
Your plan is kept in this browser. A free account keeps it with your drafts on any device: Join free · Sign in
Also: free IA self-check · A–E checklist (PDF) · have a draft? AI feedback or a review with Pete (€100)
Writing it up: how to write a Maths IA, step by step · structure and format · mistakes that cost marks · annotated exemplars, marked on every criterion
Similar ideas
- Designing a working sundial for my latitudeAA SLAA HLAI SLAI HLSolid
- Measuring the Earth with a stick and a partner schoolAA SLAI SLAA HLSolid
- Why do flight paths curve on the map?AA SLAA HLAI SLAI HLAmbitious
- The hidden angles of a hip roof: 3D trigonometryAA SLAI SLAA HLSolid
All geometry & voronoi ideas · AA SL ideas · AI SL ideas · All 239 IA ideas