2 Sides, Included Angle: Challenge & Extension
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A challenging worksheet on constructing triangles using two sides and the included angle, designed for GCSE Higher students to deepen understanding and problem-solving skills.
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Full preview • 11 questions
2 Sides, Included Angle: Challenge & Extension
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Review the key concepts of constructing triangles with two sides and the included angle. Recall that to construct such a triangle, you need two lengths and the included angle between them, which guides the construction process.
B
Fluency & Practice
Answer these straightforward construction and calculation questions to practice your procedural skills.
1.
Construct a triangle with sides of 5 cm and 7 cm, and an included angle of 60°. Use the grid to draw and verify the triangle.
[3 marks]2.
Calculate the length of the third side of a triangle with two sides of 8 cm and 10 cm and an included angle of 45° using the Law of Cosines.
[3 marks]3.
Construct a triangle with sides of 6 cm and 9 cm, and an included angle of 120°. Draw accurately on the grid.
[3 marks]C
Problem Solving & Reasoning
Tackle these multi-step problems that require explanation and geometric reasoning.
1.
Given a triangle with two sides measuring 7 cm and 10 cm, and an included angle of 75°, construct the triangle. Then, find the height corresponding to the 10 cm side.
[4 marks]2.
A builder needs to construct a triangular support with two known sides of 4 m and 6 m meeting at an angle of 50°. Construct the triangle and determine the length of the third side.
[4 marks]D
Real-world Applications
Apply your knowledge to practical scenarios involving triangle construction.
1.
A surveyor needs to mark a triangular plot of land. Two sides are measured as 15 m and 20 m, with the included angle known to be 80°. Construct the triangle to scale and find the area of the plot.
[4 marks]E
Challenge & Extension
Tackle these advanced problems to deepen your understanding and extend your skills.
1.
Construct a triangle with sides of 9 cm and 12 cm, and an included angle of 135°. Then, calculate the area of the triangle using your construction.
[3 marks]2.
Prove that two triangles with sides 5, 7, and an included angle of 60°, and sides 5, 7, and an included angle of 120°, are congruent or not, based on the SAS criterion.
[3 marks]F
Mixed Review
Answer a variety of questions to consolidate your understanding of two sides and an included angle.
1.
Construct a triangle with sides of 6 cm and 8 cm and an included angle of 90°. Verify your construction by measuring on the grid.
[3 marks]2.
Calculate the angle between two sides of lengths 7 cm and 10 cm if the third side length is 12 cm, using the Law of Cosines.
[3 marks]G
Error Analysis
Review these common mistakes. Identify and correct the errors in the following statements or constructions.
1.
A student constructs a triangle with sides 4 cm and 9 cm and an included angle of 100°, but the third side measured on the grid is 7 cm. Identify the mistake and explain how to correct it.
[4 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)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet