Using Trigonometry

Real Trigonometry

Trigonometry Use
Updated June 2017

Trigonometry: use in finding heights

These excellent materials were designed at Leeds Metropolitan University and are excellent for seeing trigonometry in real use.

  1. Teacher/pupil task sheet with Clinometer template for angle measuring.
  2. Theodolite poster – how to use to find a height.
  3. File showing how to use theodolite: 15 pages includes answers.
  4. Another theodolite example to find height of a wall.
  5. The related YouTube channel (here) has 5 videos including one that shows how to make the clinometer (here).
  6. Instructions and template for making a trig-wheel.
  7. For interactives related to this click the Interactives tab just above – will not work on iPads and iPhones.

Trigonometry: ship’s course

Another example of a real use of trigonometry (to find a ship’s course) comes from Maths at Work, on the NCETM site (found here): includes video.

Trigonometry: height of tower at British Museum

The British Museum has a KS3 challenge to find the height of a tower in its great court (February 2016). BM KS3 Maths Challenge (includes other ideas as well).



If you use Chrome as your browser then these interactive files might not work (you are instead asked if you want to Keep or Discard the files), then Discard and go to the link here and follow the instructions to enable the relevant plugin. Mac and Windows instructions are both there: scroll down. You only have to do this once. You will need relevant permission to do this on the computer.

  1. Practise using a theodolite
  2. Angles from a tower of known height
  3. Angles on a straight line
  4. Find missing angles quiz

Practical lesson

  1. Create clinometers or borrow theodolites. Borrow long tapes from PE, use metre rules or laser distance measures.
  2. Go outside and have pupils stand different distances away from eg the school building (if you can).
  3. Measure distance from school building, use clinometer to find angle, take distance of height of clinometer above ground level.
  4. Have each pupil calculate height of building and then use mean, mode or median to decide ‘height’.
  5. Consider rounding, accuracy, think about which errors of measurement have the biggest impact.
  6. Think about other ways to find the height of the building – could any of these be more accurate?
  7. Find true height of building from building plans!
  8. With brick buildings finding the height of e.g. 10 layers of bricks is usually the most accurate method.