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Unit 34 Pythagoras’ Theorem and Trigonometric Ratios

Unit 34 Pythagoras’ Theorem and Trigonometric Ratios. Unit 34. 34.1 Pythagoras’ Theorem. Pythagoras’ theorem states that for any right angled triangle. Example 2 Find the length of side x. Solution. Example 1 What is the length of a (the hypotenuse)? Solution. ?. ?. ?. ?. ?. ?.

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Unit 34 Pythagoras’ Theorem and Trigonometric Ratios

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  1. Unit 34Pythagoras’ Theorem and Trigonometric Ratios

  2. Unit 34 34.1 Pythagoras’ Theorem

  3. Pythagoras’ theorem states that for any right angled triangle. Example 2 Find the length of side x. Solution Example 1 What is the length of a (the hypotenuse)? Solution ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  4. Unit 34 34.2 Using Pythagoras’ Theorem

  5. Here we see how Pythagoras’ Theorem can be used to solve different problems. D 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 C ? ? ? ? ? ? ? ? B A ? ? ? ? ? ? ? ? ? ? ? ?

  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 θstate which side is • Hypotenuse CB • Adjacent AC • 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 • The length of FI • The length of EI • The area of EFGH Solution (a) (b) (c) ? ? ? ? ? ? ? ? ? ? ?

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