AC9M10M03
solve practical problems applying Pythagoras’ theorem and trigonometry of right-angled triangles, including problems involving direction and angles of elevation and depression
Elaborations
- AC9M10M03_E1applying 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
- AC9M10M03_E2applying 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
- AC9M10M03_E3using a clinometer to measure angles of inclination, and applying trigonometry, and proportional reasoning to determine the height of buildings in practical contexts
- AC9M10M03_E4applying 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
- AC9M10M03_E5investigating 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 =√((x'-x)^2 + (y'-y)^2)
- AC9M10M03_E6exploring navigation, design of technologies or surveying by First Nations Australians, investigating geometric and spatial reasoning, and how these connect to trigonometry
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