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

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
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

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Year level 9-10
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Learning area Mathematics
Interactive Resource

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 resource

Trigonometry: finding the hypotenuse

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including sine values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using sine values to calculate the length of a hypotenuse in triangles. For example, ...

Teacher resource

What is trigonometry and where would you use it?

Use these tasks and resources to provide opportunities for students to apply understandings about trigonometry. Students investigate the relationship between sine and cosine as the angle value changes from 0 to 90 degrees in a right-angled triangle.

Interactive resource

Trigonometry: cosine

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right angle triangle within a unit circle (radius of one unit). Identify the cosine ratio and enter the cosine values of angles from 0–90 degrees into a table. Answer questions about the cosine values. This learning object ...

Moving Image

Elevated or depressed about trigonometry?

Learn how to solve the trigonometry problems in this video using sine, cosine and tangent. In order to solve problems with angles of depression, don't forget that alternate angles - when two parallel lines are crossed with a transversal - are equal. Now you're set!

Moving Image

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 Resource

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.

Moving Image

Finding the missing angle of a triangle

Do you know to use trigonometry to find the unknown angle of a triangle? See how to do this with a right-angled triangle. All you need is the length of two sides. Find out which trig ratio to use in these three examples. You'll notice that the inverse of sine, cosine and tangent will be used, so have your calculator at ...

Interactive Resource

Trigonometric Ratios

An animated introduction to the basic trigonometric ratios.

Moving Image

Trig 101: getting started!

Have you heard of trigonometry? See how to apply these labels to a right-angled triangle: angle, hypotenuse, adjacent and opposite. Find out about the three trig ratios for sine, cosine and tangent. Look out for a clever tip to remember these trig ratios! Now you are ready to apply that knowledge.

Moving Image

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 ...

Moving Image

Get your bearings using trig!

Apply your understanding of compass points (north, south, east and west) and trigonometry to solve problems about bearings and direction. Follow the steps of working out what the question is asking and drawing a labelled diagram. See how to go about solving the problem by using the correct trig ratio. In the second of these ...

Interactive Resource

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.

Moving Image

Solving problems using trig

Apply your knowledge of trigonometry to find the unknown length of one side of a triangle or one of its internal angles. Follow the steps used in two examples. First, work out what the question is asking, draw and label the right angled triangle with what you know, then use the correct trig ratio to solve the problem. One ...

Interactive resource

Trigonometry: using sine

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including sine values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using sine values to calculate side lengths in triangles. For example, find the ...

Interactive resource

Trigonometry: using tangent

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including tangent values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using tangent values to calculate side lengths in triangles. For example, find ...

Interactive resource

Trigonometry: using cosine

Solve measurement problems involving right-angled triangles by using similar triangles and trigonometric methods, including cosine values. Identify corresponding sides and ratio relationships in similar triangles. Solve measurement problems by using cosine values to calculate side lengths in triangles. For example, find ...

Interactive resource

Trigonometry: tangent

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Identify the tangent ratio and enter the tangent values of angles from 0–90 degrees into a table. Answer questions about the tangent values. This learning ...

Interactive resource

Exploring trigonometry

Label the three sides of a right-angled triangle as hypotenuse, adjacent and opposite sides. Identify which sides form a trigonometric ratio such as cosine or tangent. Watch a video showing how trigonometry is used to help planes land safely.

Video

Pythagoras's theorem: proof

This learning object includes animations of transformational geometry and algebraic proofs of Pythagoras's theorem. Interactive Illustrations of the theorem, worked examples, a quiz and practice questions are included.

Moving Image

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 ...

Interactive resource

Trigonometry: finding angles

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Set the cosine, sine and tangent values of angles from 0–90 degrees. Identify the angle for each of the values. This learning object is one in a series of ...

Interactive resource

Trigonometry: measuring with triangles

Compare the shadows cast by a small stick and a larger object such as a column of a Greek building. Check the angles at which the shadows are cast and confirm whether the two objects create similar triangles. Use equivalent ratios to calculate the lengths of a triangle's sides: the height of an object or the length of a ...

Interactive resource

Trigonometry: similar triangles

Examine pairs of right-angled triangles. Check that each pair of triangles is similar by identifying all three pairs of corresponding angles. Label corresponding angles with matching symbols. This learning object is one in a series of ten objects.