Mathematics 11–12 · Years 11–12

Height of a flagpole with a phone clinometer and a tape

Right-angled triangles (Mathematics Standard 1, Year 12); Trigonometry (Mathematics Standard 2, Year 12); Trigonometry and measure of angles: Trigonometry with acute angles (Mathematics Advanced, Year 11)

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

An angle of elevation and a measured distance fix the height of an object the learner cannot reach, and the sensitivity of tan to an angle error decides how carefully to measure.

What you need

A phone running the phyphox Inclination experiment, or a protractor clinometer with a straw and plumb line
A 50 m tape
A flagpole or building edge on level ground

How to do it

Measure the observer's eye height above the ground.
Tape a horizontal distance d of 20.0 m from the base; sight the top along the phone's edge and read the angle of elevation theta.
Compute the height H = d tan(theta) + eye height; repeat from 30 m and 40 m.
Recompute each height with the angle 1 degree lower and 1 degree higher to find the interval.
Compare the three estimates and, where a building plan gives the true height, compare with it.

What you should see

d = 20.0 m, theta = 35.0 degrees and an eye height of 1.60 m give H = 15.6 m; an angle error of plus or minus 1 degree moves the answer to 15.1 to 16.1 m, and plus or minus 0.5 degree to about plus or minus 0.26 m. The learner knows it worked when the estimates from 20, 30 and 40 m overlap within their intervals.

What changes

What you change: distance from the base d
What you measure: computed height
What you keep the same: eye height
level ground
sighting the same top point

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

The angle alone gives the height; the distance matters as much.
Standing further away always makes the answer worse; the sensitivity d sec^2(theta) depends on both d and theta, so compare the intervals.

Safety card

Low riskLearners carry it out

Hazards

walking backwards while sighting
sun in the eyes

Controls

a partner watches the ground while the observer sights
never sight towards the sun

Note

No chemicals and no heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; outdoor work follows the school's grounds or excursion risk assessment (RiskAssess where the school uses it).

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 1 focus area Right-angled triangles; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S1-04
Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 2 focus area Trigonometry; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S2-04
Mathematics Advanced 11–12 Syllabus (2024), Year 11 focus area Trigonometry and measure of angles; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-11-04
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

All Concept Studio activities