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Mathematics / Year 10 / Measurement
Curriculum content descriptions
solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression (AC9M10M03)
Elaborations
- applying right-angled trigonometry to solve navigation problems involving bearings; for example, determining the bearing and estimating the distance of the final leg of an orienteering course
- applying Pythagoras’ theorem and trigonometry to problems in surveying and design, where three-dimensional problems are decomposed into two-dimensional problems; for example, investigating the dimensions of the smallest box needed to package an object of a particular length
- using a clinometer to measure angles of inclination, and applying trigonometry, and proportional reasoning to determine the height of buildings in practical contexts
- applying Pythagoras’ theorem and trigonometry, and using dynamic geometric software, to design three-dimensional models of practical situations involving angles of elevation and depression; for example, modelling a crime scene
- investigating how autonomous vehicles use algorithms that use Pythagoras theorem and trigonometry to calculate distance and navigate spaces; for example, if an autonomous vehicle knows its current position \((x, y)\) and the coordinates of a target location \((x, y)\), it can determine the straight-line distance between them using the formula distance \(=\sqrt{(x-x)^2 + (y-y)^2}\)
- exploring navigation, design of technologies or surveying by First Nations Australians, investigating geometric and spatial reasoning, and how these connect to trigonometry
General capabilities
ScOT terms
Angles of elevation, Trigonometric ratios, Distance, Pythagoras theorem