Mathematics / Year 9 / Measurement and Geometry / Pythagoras and trigonometry

Curriculum content descriptions

Apply trigonometry to solve right-angled triangle problems (ACMMG224)

Elaborations
  • understanding the terms adjacent and opposite sides in a right-angled triangle
  • selecting and accurately using the correct trigonometric ratio to find unknown sides (adjacent, opposite and hypotenuse) and angles in right-angled triangles
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
ScOT terms

Trigonometric ratios,  Right angled triangles

Video

Catalyst: Applying trigonometry: leaning tower

The Leaning Tower of Gingin is the centrepiece of the Gravity Discovery Centre. The Catalyst team of Derek, Simon and Anja drop watermelons from the tower, to examine the rate at which they fall. They are testing Galileo's theory about falling objects. The dimensions of the tower provide an opportunity to apply some basic ...

Interactive

Finding Angles From Ratios

An animated tutorial about using a calculator to find an angle when given a trigonometric ratio. An interactive quiz is included.

Interactive

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

Interactive

Trigonometric Ratios

An animated introduction to the basic trigonometric ratios.

Online

reSolve: Gradient and Tangent

This sequence of two lessons investigates gradient and angle by applying the tangent ratio to find the angles represented by a road sign or the angle of a street. In the first lesson, students research what a road grade is and determine the actual angle of a road given its grade. They then construct their own road sign ...

Downloadable

Introduction to trigonometry

These lesson plans guide the teacher on how to introduce trigonometry to students through an investigation of similar triangles.

Text

Mathematics of bushfire

In these classroom activities students will be introduced to some of the basic mathematical principles that underpin wildfire science, with an emphasis on how theoretical concepts are used to aid our understanding of the real world, and bushfire in particular. They will learn about the complexities of the fire management ...

Online

Pythagoras and trigonometry (Measurement): Year 9 – planning tool

This planning resource for Year 9 is for the topic of Pythagoras and trigonometry. Students apply and build upon knowledge of Pythagoras’ theorem, angle properties, trigonometry and scales to solve problems involving right-angled triangles.

Video

Stateline: Mapping farmland: using area and trigonometry

In northern Queensland's Gulf region, some farmers use GPS mapping to help manage their extensive properties. Use this clip as a context for applying your understanding of area, in particular your understanding of conversion between square kilometres and hectares. Apply trigonometry and Pythagoras' theorem.

Interactive

Laptop wrap: Talking trigonometry

In this laptop-friendly resource, students consolidate their understanding of trigonometry by investigating practical applications of the ratios, highlighting the process they used to find a solution.

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Work sample Year 9 Mathematics: Similar triangles

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 9 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...

Online

TIMES Module 22: Measurement and Geometry: scale drawings and similarity - teacher guide

This is a 41-page guide for teachers. It contains an introduction to scale drawings and similarity, and in particular the tests for triangles to be considered similar. Applications of similarity are included throughout the module.

Video

ABC News: Space debris: the accuracy of space lasers

In space there are thousands of human-made objects (satellites and space junk) orbiting Earth. To avoid collision with space debris, satellites are manoeuvred out of its path. Discover how space debris is tracked using lasers, and about accuracy's effects on the lifetime of the satellite. Find out, using trigonometry, the ...

Online

Australia's population: countries of birth - dataset

The dataset provides statistics about the estimated resident population, median age and sex ratio by countries of birth for the latest year of available data. It is periodically updated by the Australian Bureau of Statistics (ABS). The dataset is included in the list of related datasets on the page in MS Excel format.

Online

Similarity

This is a website designed for both teachers and students, which addresses similarity from the Australian Curriculum for year 9 students. It contains material on enlargement transformation and similar triangles. There are pages for both teachers and students. The student pages contain interactive questions for students ...

Interactive

The geometer's warehouse

This web-based, multimedia resource focuses on the geometry of the Stage 4 and Stage 5 Mathematics syllabus. It comprises 70 dynamic html worksheets, each exploring a different outcome in Stage 4 and Stage 5 geometry.

Video

My Five Cents: Why borrowing can cost you more

Think credit cards are basically free money? Gen Fricker will make you think again. Learn how interest rates and fees affect the money you borrow, and why they may be more expensive in the long run. Oh dear! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

Video

MathXplosion, Ep 50: How to use a tetrahedron to solve the tree problem

How can you place four trees exactly the same distance apart from one other? By making a model! By using miniature trees to make a model of the problem, it becomes clear that a 2D solution is impossible. We learn how objects can help us visualise the problem situation, which in this case requires a 3D solution: a tetrahedron.

Online

Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

Video

Modelling climate changes

There is a saying: 'climate is what you expect and weather is what you get'. |Understanding climate change is very difficult for most people, especially when the weather we experience is different from the information we are given by scientists about the climate changing. The difference is that weather reflects short-term ...