Mathematics / Year 10 / Measurement and Geometry / Pythagoras and trigonometry

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

Solve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245)

Elaborations
  • applying Pythagoras Theorem and trigonometry to problems in surveying and design
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
ScOT terms

Angles,  Right angled triangles

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 ...

Teacher resource

Secondary mathematics: using real data

These seven learning activities, which focus on the use of 'real data' 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 the three content strands ...

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 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.

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 ...

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.

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, ...

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: 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: 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: 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

Trig degrees

Use a unit circle tool to explore sine, cosine and tangent values in different quadrants. Determine the values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of the graphs and the values for the functions in different quadrants. Observe the graphs animate and ...

Interactive resource

Trig degrees: sine to 360

Use a unit circle tool to explore sine values in different quadrants. Determine the sin Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of sin Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and table ...

Interactive resource

Trig degrees: tangent to 360

Use a unit circle tool to explore tangent values in different quadrants. Determine the tan Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of tan Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and ...

Interactive resource

Trig degrees: cosine to 360

Use a unit circle tool to explore cosine values in different quadrants. Determine the cos Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of cos Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and table ...

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

Congruent triangles

Find out about congruent and non-congruent triangles and the conditions required to make them. Use line segments and angles to build two congruent triangles for three different combinations of sides and angles. Explore the SSS case (side, side, side), the SAS case (two sides and the included angle) and the ASA case (two ...