c² = a² + b²: Challenge & Extension
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focusing on applying the Pythagoras Theorem c² = a² + b² to find the hypotenuse in various contexts, including problem solving, real-world applications, and extension questions.
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c² = a² + b²: Challenge & Extension
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working clearly in the grid spaces provided.
1.
Calculate the hypotenuse c of a right-angled triangle with sides a = 3 cm and b = 4 cm.
[2 marks]2.
A ladder leans against a wall, reaching a height of 12 meters. The base of the ladder is 5 meters from the wall. Calculate the length of the ladder.
[3 marks]3.
A right-angled triangle has sides a = 7 m and c = 25 m. Find the length of side b.
[3 marks]4.
Construct a right-angled triangle with a hypotenuse of 10 units and one side of length 6 units. Label all sides.
[4 marks]5.
A rectangular garden has a length of 20 meters and a width of 12 meters. Find the length of the diagonal pathway across the garden.
[2 marks]6.
A triangle has sides of 9 cm and 12 cm. The hypotenuse is unknown. Calculate its length.
[2 marks]7.
In a right-angled triangle, the hypotenuse c = 13 units, and side a = 5 units. Find side b.
[2 marks]8.
A boat crosses a river 8 km wide. The boat takes a diagonal path with a hypotenuse of 10 km. Calculate the shortest distance downstream (the other side).
[3 marks]9.
A square-based pyramid has a slant height of 15 m. The base side length is unknown, but the height is 9 m. Calculate the length of the base side if the slant height forms a right triangle with half the base length and the height.
[4 marks]10.
A developer designs a triangular support structure with sides 8 m, 15 m, and c. Use Pythagoras to determine if it is a right-angled triangle, and identify the hypotenuse.
[3 marks]11.
Identify and correct the mistake: A student claims that in a right triangle with sides 6 and 8, the hypotenuse is 10. Is this correct? Why or why not?
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet