# reSolve: Trigonometric Trajectories

TLF ID M025326

In this sequence of two lessons, students investigate trigonometric and Pythagorean relationships through two contexts: researching and building a model zipline ride and outlining a proposal for glider poles. In the first lesson, students apply trigonometric and Pythagorean relationships to investigate the dimensions of ziplines around the world. They then plan, diagram, model and construct a zipline for a doll. In the second lesson, they investigate how 'glider poles' allow gliding mammals to cross wide roads. They design a pair of glider poles appropriate for the animals and roads in their region using their knowledge of trigonometry, particularly angles of elevation and depression. The lessons are outlined in detail including curriculum links, vocabulary, sample answers, discussion points and student resources. This sequence is part of the reSolve: Maths by Inquiry program.

#### Educational details

Educational value
• This resource is very valuable for the year 10 mathematics content descriptions about solving right-angled triangle problems including those involving direction and angles of elevation and depression. Throughout the investigations, students are challenged to use right-angle triangles to determine angles of depression and elevation as they plan, design and model their zipline and glider poles.
• The resource is also of some value for the year 10A mathematics content description about applying Pythagoras' Theorem and trigonometry to solve three-dimensional problems in right-angled triangles. Although the resource does not explicitly address this content description, it could be used to extend the problem to challenge students to design a glider pathway using an arrangement of poles that would require three-dimensional geometry.
• This resource also offers opportunities to link to the Numeracy General capability, as students visualise, describe and analyse the way the triangles formed by ropes, poles and trajectories are combined and positioned in the environment for their ziplines and glider pathways to be optimised.
• This resource is also of pedagogical value as it supports teachers in building an inquiry-focused learning environment with authentic application of mathematical skills and understandings. The unit aims to develop content knowledge as well as assisting students to understand the process of inquiry.
Year level

10

Learning area
• Mathematics

#### Other details

Contributors
• Contributor
• Name: Education Services Australia
• Organization: Education Services Australia
• Description: Data manager
• URL: http://www.esa.edu.au/
• Name: Australian Government Department of Education and Training
• Organization: Australian Government Department of Education and Training
• Publisher
• Name: Australian Academy of Science
• Organization: Australian Academy of Science
• Description: Publisher
• URL: https://www.science.org.au/
• Name: Education Services Australia Ltd
• Organisation: Education Services Australia Ltd
• URL: www.esa.edu.au
Access profile
• Unknown
Learning Resource Type
• Online
Rights
• © Australian Government Department of Education and Training 2017. Unless otherwise indicated, this material may be used in accordance with the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.