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

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Curriculum content descriptions

Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222)

Elaborations
  • understanding that Pythagoras' Theorem is a useful tool in determining unknown lengths in right-angled triangles and has widespread applications
  • recognising that right-angled triangle calculations may generate results that can be integers, fractions or irrational numbers
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
ScOT terms

Pythagoras theorem

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Year level 9-10
Resource type
Learning area Mathematics
Interactive resource

Exploring the Pythagorean theorem

Adjust the dimensions of a right-angled triangle. Calculate the area of squares bordering each side of the triangle. Notice that the area of the square bordering the hypotenuse is equal to the sum of the areas of the squares bordering the other two sides. Watch a video showing how Pythagoras's theorem is used to determine ...

Teacher resource

reSolve: Pythagoras' Theorem

This sequence of lessons challenges students to apply Pythagoras' Theorem to explore practical and historical real-world problems. In the first lesson students investigate the connection between their solutions and concepts of symmetry and algebra. In the second lesson, they explore technology reliant on mathematical concepts. ...

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

Pythagoras' theorem

This is an interactive resource that provides a visual demonstration of one geometrical proof of Pythagoras' theorem. The activity, which can be accessed from the home screen, allows right-angled triangles to be manipulated to show the relationship between the squares of the side lengths. This resource is one of a series ...

Moving Image

Mystery man Pythagoras meets his match

What do you know about Pythagoras? Join Vi Hart as she not only explains his theorem but raises some legends about his dark past! Follow Vi's timeline of famous mathematicians to find out in which century Pythagoras lived. See how Vi shows a proof of his theorem and raises what was a big dilemma for Pythagoras: the irrational ...

Moving Image

Pythagorean triangles

How did the ancient Egyptians construct buildings with right-angled corners? Join Marcus du Sautoy as he describes one method that might have been used. Find out how it involves a triangle with sides that have a ratio 3:4:5.

Moving Image

Finding the missing side of a triangle

Know how to use trigonometry to find the unknown length of one side of a triangle? See how to do this with a right-angled triangle. All you need is an internal angle and the length of one side. Find out which trig ratio to use in three examples. Which one requires the use of cosine? Also look out for a clever tip to remember ...

Text

Indigo Interior

This resource is a web page containing a problem solving task that requires an understanding of Pythagoras' theorem. The task involves finding the area of shaded region with a circle with a known area. To solve the problem students need to establish a right angled triangle and apply Pythagoras' theorem. A printable resource ...

Text

BBC Bitesize: Pythagoras's theorem - revision

In these illustrated information sheets, Pythagoras's theorem is stated and students revise its application to proving whether or not a triangle is right-angled. Students find the length of one side of a right-angled triangle when the other two sides are known. Pythagoras's theorem is applied to find the distance between ...

Moving Image

Pythagoras frets about music

Pythagoras is well known for his theorem about right-angled triangles. Find out about his connection to music and how he linked mathematics to patterns in musical notes to create the musical scale. Do your own investigation into subdividing a vibrating string and experimenting with ratios. See why an octave is divided into ...

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: 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: 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: 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: 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: 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: 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: 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: 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 ...