a² = c² - b²: Real-world Applications in Architecture & Design
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the use of a² = c² - b² within real-world contexts such as architecture and design, aimed at GCSE Higher students.
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a² = c² - b²: Real-world Applications in Architecture & Design
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the shorter side length of a triangular wall if the hypotenuse is 15 meters and the other side is 9 meters, using a² = c² - b².
[2 marks]2.
A designer needs to determine the length of a diagonal support in a frame. The support forms a right-angled triangle with a base of 8 meters and hypotenuse of 10 meters. Find the length of the support using a² = c² - b².
[3 marks]3.
In constructing a ramp, the hypotenuse measures 13 meters and one side is 5 meters. Use a² = c² - b² to find the length of the other side.
[2 marks]4.
A wall design includes a rectangular panel with a diagonal length of 20 meters and one side measuring 16 meters. Calculate the other side of the panel.
[3 marks]5.
A triangular support in a building has a hypotenuse of 25 meters and one leg of 15 meters. Find the length of the other leg.
[3 marks]6.
Construct a right-angled triangle on the grid with a hypotenuse of 12 units and one side of 5 units. Use a² = c² - b² to determine the length of the other side.
[4 marks]7.
A designer is creating a triangular support with a hypotenuse of 18 meters and one side of 7 meters. Calculate the other side length.
[3 marks]8.
In a bridge structure, a diagonal brace forms a right triangle with the vertical and horizontal supports. If the diagonal measures 30 meters and the horizontal support is 24 meters, find the vertical support length.
[3 marks]9.
A building engineer needs to determine the length of a support beam that forms a right triangle with a known hypotenuse of 14 meters and one leg of 10 meters. Find the length of the support beam.
[2 marks]10.
A complex architectural feature involves a support with a hypotenuse of 24 meters and one leg of 17 meters. Calculate the other leg.
[3 marks]11.
Identify and correct the mistake in this calculation: If a hypotenuse is 10 meters and one side is 6 meters, then the other side is 8 meters, using a² = c² - b².
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet