a² = c² - b²: Challenge & Extension
Mathematics
GCSE Higher
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the formula a² = c² - b², used to find the shorter side in right-angled triangles. Suitable for GCSE Higher students looking to deepen understanding and apply the concept in various contexts.
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a² = c² - 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 in the grid spaces provided.
1.
Calculate the length of side a in a right-angled triangle where the hypotenuse c is 13 units and side b is 5 units.
[3 marks]2.
A triangle has sides c = 10 units and b = 6 units. Find side a.
[3 marks]3.
Construct a right-angled triangle on the grid with hypotenuse c = 15 units and side b = 9 units. Use the formula a² = c² - b² to find the length of side a.
[4 marks]4.
In a right-angled triangle, if side a is 7 units and side c is 25 units, find side b.
[3 marks]5.
A ladder leans against a wall, reaching 9 meters high. The foot of the ladder is 12 meters from the base of the wall. Find the length of the ladder.
[4 marks]6.
A rectangular garden has a diagonal of 20 meters. The length is 16 meters. Find the width using a² = c² - b².
[3 marks]7.
Given c = 17 and a = 8, calculate side b.
[3 marks]8.
A ramp forms a right-angled triangle with hypotenuse 14 meters and height 10 meters. Find the length of the base.
[3 marks]9.
A projection shows a triangle with sides c = 20 units and b = 12 units. Find side a.
[3 marks]10.
Identify and correct the mistake in this calculation: a = √(c² - b²), where c = 10 and b = 8, giving a = 2.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet