Pythagoras’ Theorem And Trigonometry
Overview
Pythagoras' theorem and trigonometry are not limited to flat triangles: they work in three dimensions too. The trick is to find the right right-angled triangle inside a solid, often by using a diagonal of a face as a stepping stone to the diagonal of the whole solid.
In this lesson (Extended tier) you will solve three-dimensional problems using Pythagoras' theorem and trigonometry, including finding the angle between a line and a plane.
Objectives
- Carry out calculations and solve problems in three dimensions using Pythagoras’ theorem and trigonometry, including calculating the angle between a line and a plane.
Audio Lesson
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Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Pythagoras’ Theorem And Trigonometry. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- A cuboid is 4 by 3 by 12. What is the diagonal of the 4 by 3 base? A. 5 B. 7 C. 12 D. 13 Answer: A
- Using a base diagonal of 5 and height 12, the space diagonal is: A. 12 B. 13 C. 17 D. 169 Answer: B
- To find a space diagonal of a cuboid you apply Pythagoras: A. once B. twice C. three times D. not at all Answer: B
- The angle between the space diagonal and the base (height 12, base diagonal 5) is: A. 22.6° B. 45.0° C. 67.4° D. 90.0° Answer: C
- The angle between a line and a plane is measured between the line and: A. the vertical B. its projection on the plane C. any edge D. the diagonal Answer: B
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Practice Mock Questions
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