2 Sides, Included Angle: Mixed Review
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet providing mixed review questions on constructing triangles using two sides and the included angle (SAS). Suitable for Year 9 students to practice procedural skills, reasoning, and real-world applications.
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Full preview • 14 questions
2 Sides, Included Angle: Mixed Review
Subject: MathematicsGrade: Year 9
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Date:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Construct a triangle with sides 6 cm and 8 cm, and an included angle of 60°. Use the grid to draw accurately.
[3 marks]2.
Given two sides of lengths 5 m and 7 m with an included angle of 45°, calculate the length of the third side.
[3 marks]3.
Construct a triangle with sides 4.5 cm and 6.5 cm, and an included angle of 120°. Show your construction on the grid.
[3 marks]4.
Using the Law of Cosines, find the missing side when two sides of lengths 9 cm and 10 cm include an angle of 75°.
[4 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working and reasoning.
1.
A surveyor needs to construct a triangle with two known sides of 50 m and 80 m, and the included angle is 40°. Explain step-by-step how the surveyor would construct this triangle on the ground.
[4 marks]2.
If in a triangle two sides are 7 cm and 9 cm with an included angle of 105°, determine whether the third side is longer or shorter than 10 cm using the Law of Cosines.
[3 marks]3.
Describe a real-world scenario where constructing a triangle with two sides and an included angle would be necessary, and explain the steps involved.
[4 marks]4.
Construct a triangle with sides 3 cm and 7 cm, and an included angle of 150°. Using the grid, verify the accuracy of your construction.
[3 marks]5.
Using the Law of Cosines, find the angle between sides of 8 m and 10 m when the third side is 6 m.
[4 marks]C
Real-world Applications
Answer all questions. Show your working.
1.
A drone pilot needs to determine the distance between two locations 100 m apart, with a known angle of 70° between the drone's line of sight to each point. How can the pilot construct this scenario and find the distance?
[4 marks]2.
A triangle has two sides measuring 12 m and 16 m with the included angle of 85°. Calculate the area of the triangle.
[3 marks]D
Challenge & Extension
Attempt these challenging questions. Show detailed working.
1.
Construct a triangle with sides 10 cm and 15 cm, and an included angle of 30°. Now, calculate the length of the third side using the Law of Cosines, and verify your construction accuracy.
[4 marks]2.
Given two sides of 8 cm and 12 cm, and an included angle of 90°, construct the triangle. Then, derive a general formula for calculating the third side when the included angle is variable, using the Law of Cosines.
[4 marks]E
Error Analysis
Review the following common mistake and identify the error. Correct it and explain your reasoning.
1.
A student constructs a triangle with sides 5 cm and 9 cm, and an included angle of 60°, but reports the third side as 10 cm. Identify the mistake made in this calculation or construction, and provide the correct value with explanation.
[3 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