Math unit34 pythagoras' theorem and trigonometric ratios
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The document covers Pythagoras' theorem and trigonometric ratios, detailing methods to find side lengths in right-angled triangles. It includes various examples for understanding and applying the theorem, as well as definitions for sine, cosine, and tangent ratios. The content is structured across multiple presentations, providing step-by-step solutions to the problems.
Math unit34 pythagoras' theorem and trigonometric ratios
- 1. Unit 34 Pythagoras’ Theorem and Trigonometric Ratios Presentation 1 Pythagoras’ Theorem Presentation 2 Using Pythagoras’ Theorem Presentation 3 Sine, Cosine and Tangent Ratios Presentation 4 Finding the Lengths of Sides in Right Angled Triangles
- 2. Unit 34 34.1 Pythagoras’ Theorem
- 3. Pythagoras’ theorem states that for any right angled triangle. Example 1 What is the length of a (the hypotenuse)? Solution ?? ? ?? ?? Example 2 Find the length of side x. Solution ? ? ?? ?? ? ? ?
- 4. Unit 34 34.2 Using Pythagoras’ Theorem
- 5. Example 1 Find the length of the side marked x in the diagram. Solution In triangle ABC In triangle ACD Example 2 Find the value of x as shown in the diagram, giving the lengths of the two unknown sides Solution Pythagoras’ Theorem gives So Here we see how Pythagoras’ Theorem can be used to solve different problems. ? ?? ??? ?? ? ? ? ?? ? ?? ? ? ? ? C BA D
- 6. Unit 34 34.3 Sine, Cosine and Tangent
- 7. For a right angled triangle, the sine, cosine and tangent of the angle θ are defined as:
- 8. Example 1 For the triangle and angle θ state which side is (a)Hypotenuse CB (b)Adjacent AC (c)Opposite AB ? ? ?
- 9. Example 2 For the triangle below, what is the value of (a) (b) (c) ? ? ? ? ? ? ? ? ?
- 10. Unit 34 34.4 Finding the Lengths of sides in Right Angled Triangles
- 11. Example 1 Find the length of the side marked x in the triangle. Solution So ? ? ? ?? (to 1 d. p.)
- 12. Example 2 Find the length of the side marked x in the triangle Solution So ? ? ? ?? (to 1 d. p.)
- 13. Example 3 For the diagram calculate to 3 significant figures (a) The length of FI (b) The length of EI (c) The area of EFGH Solution (a) (b) (c) ? ? ? ? ? ? ? ? ? ? ?