a² = b² + c² - 2bc cosA: Problem Solving & Reasoning
Mathematics
GCSE Higher
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on applying the cosine rule a² = b² + c² - 2bc cosA to solve problems involving finding side lengths in triangles. Includes practice, reasoning, real-world scenarios, and extension questions.
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a² = b² + c² - 2bc cosA: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the length of side a in a triangle where b = 7 cm, c = 10 cm, and the included angle A = 60°.
[3 marks]2.
In triangle ABC, side b = 5 m, side c = 9 m, and angle A = 45°. Find side a.
[3 marks]3.
A triangle has sides b = 8 units, c = 6 units, and angle A = 30°. What is the length of side a?
[3 marks]B
Problem Solving & Reasoning
Answer all questions with detailed working. Use the grid where appropriate.
1.
A kite-shaped triangle has sides b = 9 cm and c = 12 cm. The included angle A is 75°. Find the length of side a, explaining each step of your calculation.
[4 marks]2.
In triangle PQR, side b = 10 m, side c = 14 m, and angle A = 40°. Calculate side a and justify your method.
[4 marks]3.
A surveying team measures two sides of a triangle as 50 m and 70 m with an included angle of 60°. Find the third side, explaining the steps involved.
[4 marks]C
Real-world Applications
Answer the following questions based on real-life contexts. Show all working.
1.
A drone flies from point A to point B, where the distance between A and B is 8 km. The drone then moves to point C such that angle BAC is 120°, and sides AB = 8 km, AC = 6 km. Find the straight-line distance from A to C.
[4 marks]2.
A radio tower is 50 meters tall. A person standing 100 meters from the tower sights the top of the tower at an angle of elevation of 30°. Calculate the approximate height of the tower above ground level.
[4 marks]D
Challenge & Extension
Attempt these more difficult problems. Show comprehensive working.
1.
A triangle has sides b = 13 cm and c = 15 cm, with angle A = 70°. Find side a, then verify your answer by calculating the possible other side length if the triangle were to be flipped (considering the law of cosines).
[4 marks]2.
Determine the possible lengths of side a in a triangle where sides b and c are 9 cm and 14 cm respectively, and angle A is 150°. Explain the reasoning behind your answer.
[4 marks]E
Mixed Review
Solve these varied questions to consolidate your understanding.
1.
Given sides b = 6 cm, c = 8 cm, and angle A = 90°, find side a using the cosine rule and compare your result with the Pythagorean theorem.
[3 marks]2.
In triangle XYZ, sides b and c are 7 m and 9 m, with angle A = 100°. Calculate side a and determine if the triangle is obtuse.
[3 marks]F
Error Analysis
Review the common mistakes shown below and identify what is wrong or missing in the solution. Correct the error and justify your correction.
1.
A student calculates side a as 12 cm using the cosine rule with b = 8 cm, c = 10 cm, and angle A = 60°, but the answer is incorrect. Identify the mistake and provide the correct calculation.
[2 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet