1. Unit 34 Pythagoras’ Theorem and Trigonometric Ratios Presentation 1Pythagoras’ Theorem Presentation 2Using Pythagoras’ Theorem Presentation 3Sine, 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 B A 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)HypotenuseCB (b)AdjacentAC (c)OppositeAB ? ? ?

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) ? ? ? ? ? ? ? ? ? ? ?