IA idea · Geometry, trigonometry & Voronoi diagrams

Which method measures a building's height most accurately?

AA SLAI SL Accessible Also in: Statistics

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?

Adapt it: change the place, the data or the comparison until the question is yours.

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

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

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.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

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.

Taking it further

Use calculus to find the distance that minimises the height error for a given angle error.

Turn this idea into your IA

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