AQA · Mathematics · 8300
GCSE Maths: Pythagoras: show triangle is right angle
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Pythagoras: show triangle is right angle (Corbettmaths Video 261), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is Pythagoras' theorem used to calculate?
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The length of a side in a right-angled triangle when the other two sides are known.
A ladder is 4 metres long and its base is 1.5 metres from a wall. How do you find how far up the wall it reaches?
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Use Pythagoras' theorem: the height up the wall is √(4² - 1.5²).
How do you test whether a triangle is right-angled using its side lengths?
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Check if the square of the longest side equals the sum of the squares of the other two sides (a² + b² = c²).
In an isosceles triangle, how can you use Pythagoras' theorem to find the height?
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Drop a perpendicular from the apex to the base. This bisects the base, creating two right triangles where you can apply Pythagoras.
A rectangle is 20 cm long and 8 cm wide. What method finds the diagonal length?
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Use Pythagoras' theorem: diagonal = √(20² + 8²).
If a right triangle has sides 14 cm and 18 cm, why are there two possible lengths for the third side?
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Because it's unclear which is the hypotenuse. The third side could be √(18² - 14²) or √(18² + 14²).
What common mistake involves adding a² and b² when using Pythagoras' theorem?
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Forgetting to take the square root at the end: writing c = a² + b² instead of c = √(a² + b²).
An airplane flies 50 miles east then 180 miles south. How do you find the direct distance?
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Use Pythagoras' theorem: direct distance = √(50² + 180²).
For a square with side length 5 cm, how do you find the diagonal length?
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Use Pythagoras' theorem: diagonal = √(5² + 5²) = 5√2 cm.
A triangle has sides of 4 cm, 6 cm, and 7 cm. Is it right-angled?
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No. Check: 4² + 6² = 16 + 36 = 52, but 7² = 49. Since 52 ≠ 49, it is not right-angled.
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