Sine And Cosine Formulae
Overview
Not every triangle contains a right angle, so SOHCAHTOA alone is not enough. The sine rule and the cosine rule let you find missing sides and angles in any triangle, making them essential tools across the entire 4PM1 specification and beyond.
You will learn when to reach for each rule, handle the ambiguous case that the sine rule can produce, and calculate areas without needing a perpendicular height. Every worked example follows the method examiners reward: identify the known quantities, choose the right formula, substitute, and solve with clear working.
Objectives
- Use the sine rule and cosine rule to solve problems in triangles
- Use the formula (1/2)*ab*sin(C) for the area of a triangle
Mind map
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Sine And Cosine Formulae. 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.
- When should you use the cosine rule instead of the sine rule? A) When you know two angles and one side B) When you know two sides and the included angle C) When you know one side and its opposite angle D) When you know all three angles Answer: B
- In a triangle with a = 5, b = 7 and C = 60 degrees, what is a squared + b squared - 2ab cos C? A) 39 B) 74 C) 25 D) 49 Answer: A
- The ambiguous case of the sine rule can arise when you are given: A) Three sides B) Two angles and a side C) Two sides and a non-included angle D) Two sides and the included angle Answer: C
- What is the area of a triangle with sides 6 cm and 10 cm and an included angle of 30 degrees? A) 15 cm squared B) 30 cm squared C) 60 cm squared D) 25.98 cm squared Answer: A
- In a triangle ABC, if a/sin A = 12, what is b when B = 45 degrees? A) 12 B) 6 sqrt(2) C) 6 D) 12 sqrt(2) Answer: B
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Practice Mock Questions
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