a² = b² + c² - 2bc cosA: Mixed Review
Mathematics
Year 9
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the use of the Cosine Rule to find side lengths in triangles, including procedural practice, problem solving, real-world applications, and extension questions.
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a² = b² + c² - 2bc cosA: Mixed Review
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In triangle ABC, sides b = 7 cm, c = 9 cm, and angle A = 60°. Calculate the length of side a using the Cosine Rule.
[3 marks]2.
Given sides b = 5 cm, c = 8 cm, and side a = 9 cm, find the measure of angle A in degrees.
[4 marks]3.
Calculate side a in a triangle where sides b = 6 cm, c = 10 cm, and angle A = 45°. (Round to one decimal place)
[3 marks]4.
A triangle has sides b = 8 cm, c = 6 cm, and angle A = 30°. Find side a.
[3 marks]5.
Construct a triangle with sides approximately 7 cm, 9 cm, and an included angle of 75°. Use the Cosine Rule to verify the length of the third side.
[4 marks]6.
In triangle PQR, sides p and q are both 10 cm, and the included angle R is 120°. Find side r.
[3 marks]7.
A boat is 5 km from a lighthouse. The angle between the boat's line of sight to the lighthouse and the shoreline is 70°. How far is the boat from the shoreline?
[4 marks]8.
A surveyor measures two sides of a triangular plot as 20 m and 25 m, with the included angle of 100°. Calculate the third side.
[4 marks]9.
A triangle has sides 12 cm and 15 cm, with an included angle of 60°. Find the length of the third side.
[3 marks]10.
Identify and correct the mistake: A student uses the formula a² = b² + c² + 2bc cosA to find side a in a triangle. Why is this incorrect?
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet