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Pythagoras and right-triangle calculations topic check

Practise pythagoras and right-triangle calculations in G1 Mathematics, check independently, and return later to review. This check covers selected skills, not the whole course topic.

Learning goals

Calculate a hypotenuse from two perpendicular lengths
Calculate a shorter side from a hypotenuse and another side
Test the Pythagorean equality using the longest side
Use and justify Pythagoras’ theorem
Choose a right-triangle ratio and calculate a side
Choose a right-triangle ratio and calculate an acute angle
Calculate a trigonometric height difference and the height from its reference

G1 Mathematics 2027

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Choose a practice setCalculate a hypotenuse from two perpendicular lengths · 4 questionsCalculate a shorter side from a hypotenuse and another side · 4 questionsTest the Pythagorean equality using the longest side · 4 questionsChoose a right-triangle ratio and calculate a side · 6 questionsChoose a right-triangle ratio and calculate an acute angle · 6 questionsCalculate a trigonometric height difference and the height from its reference · 4 questionsAll skills in this check

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Practise

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Check your progress

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Calculate a hypotenuse from two perpendicular lengths · Check your progress

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Calculate a shorter side from a hypotenuse and another side · Check your progress

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Test the Pythagorean equality using the longest side · Check your progress

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Choose a right-triangle ratio and calculate a side · Check your progress

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Choose a right-triangle ratio and calculate an acute angle · Check your progress

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Calculate a trigonometric height difference and the height from its reference · Check your progress

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Check again

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Calculate a hypotenuse from two perpendicular lengths · Check again

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Calculate a shorter side from a hypotenuse and another side · Check again

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Test the Pythagorean equality using the longest side · Check again

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Choose a right-triangle ratio and calculate a side · Check again

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Choose a right-triangle ratio and calculate an acute angle · Check again

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Calculate a trigonometric height difference and the height from its reference · Check again

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Retention check

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Calculate a hypotenuse from two perpendicular lengths · Retention check

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Calculate a shorter side from a hypotenuse and another side · Retention check

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Test the Pythagorean equality using the longest side · Retention check

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Choose a right-triangle ratio and calculate a side · Retention check

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Choose a right-triangle ratio and calculate an acute angle · Retention check

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Calculate a trigonometric height difference and the height from its reference · Retention check

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Practise: Calculate a hypotenuse from two perpendicular lengths

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Practise: Calculate a shorter side from a hypotenuse and another side

Practise questions on the skills you are learning.

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Practise: Test the Pythagorean equality using the longest side

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Practise: Choose a right-triangle ratio and calculate a side

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Practise: Choose a right-triangle ratio and calculate an acute angle

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Practise: Calculate a trigonometric height difference and the height from its reference

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Revision notes

Revise trigonometry

Use Pythagoras and its converse, then choose sine, cosine or tangent from the sides and acute angle of a right triangle.

Key ideas

Pythagoras and its converse
Use the side opposite a right angle and test whether three lengths form a right triangle.
Right-triangle sine, cosine and tangent
Name sides relative to the chosen acute angle and choose a ratio using the available quantities.

What the syllabus asks

From the G1 Mathematics 2027 syllabus

Use of Pythagoras’ theorem
Determining whether a triangle is right-angled given the lengths of three sides
Use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles (including problems involving angles of elevation and depression)