Some Intermediate students have been learning complex mathematics to measure the heights of different structures.

We have been lucky to have Robert Wilson coming in to teach a small group about the real-world uses of trigonometry. They have learned to make and use clinometers to measure the heights of structures. The small group have then taught the rest of the class their learning to share this knowledge.

The way it works is this: If they know the height of the person measuring (to their eyeball!) and the distance they are away from the object, then they can measure the angle from their eye to the top of the structure (using the clinometer). They then find the tangent of the angle and multiply by the distance they were away and add the height the measurement was taken (to their eyeball) - simple!!

They have been challenged to come up with the most accurate measurement for the height of different objects around the school and will be using averages to hone their precision.

Some applications of this mathematics are:

• Surveying, to measure an angle of inclination or elevation.
• Measuring angles of elevation, slope, or incline, e.g. of an embankment.
• Measuring movements in walls or the ground in civil engineering projects.
• Some automotive safety systems.
• Monitoring the boom angle of cranes.
• Measuring the "look angle" of a satellite antenna towards a satellite.
• Adjusting a solar panel to the optimal angle to maximise its output.
• Measuring the height of a building, tree, or other feature using a vertical angle and a distance (determined by taping or pacing), using trigonometry.
• Measuring the list of a ship in still water and the roll in rough water.
• Measuring steepness of a ski slope.
• Measuring range of motion in the joints of the body.
• Setting firing angle of a cannon or gun (determines projectile range)