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

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

Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223)

Elaborations
  • developing understanding of the relationship between the corresponding sides of similar right-angled triangles
General capabilities
  • Numeracy Numeracy
ScOT terms

Trigonometric ratios,  Right angled triangles,  Similarity (Geometry)

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Year level 9-10
Resource type
Learning area Mathematics
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: 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 ...

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: 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 ...

Teacher resource

Trigonometry

This is a website designed for both teachers and students, which addresses content on trigonometry from the Australian Curriculum for year 9 students. It contains material on working with the similarity of right-angled triangles, the three basic trigonometric ratios, and solving problems with trigonometry. There are pages ...

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: 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

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.

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.

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 ...

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, ...

Interactive resource

Trigonometry: sine

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). Find corresponding sides in similar triangles and find relationships between ratios. Identify the sine ratio and enter the sine values of angles from 0–90 ...

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

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

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 ...

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.

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

The Cartesian plane

This is a four-page HTML resource about solving problems involving the Cartesian plane. It contains three videos and four questions for students to complete. The resource discusses and explains the use of coordinates and finding the distance between two points.

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

Trigonometric Ratios

An animated introduction to the basic trigonometric ratios.