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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 Unit 34 34.1 Pythagoras’ Theorem Pythagoras’ theorem states that for any right angled triangle. 2 ExampleExample 1 the length of side x. What is Find the length of a (the hypotenuse)? SolutionSolution ?? ? ? ? ?? ? ? ? ? ? ? ? ? ? Unit 34 34.2 Using Pythagoras’ Theorem Here we see how Pythagoras’ Theorem can be used to solve different problems. D Example 12 Find the length ofxthe marked value of as side shown in thex in the diagram. diagram, giving the lengths of the two unknown sides Solution In triangle ABC Solution ? ? ?? ? C Pythagoras’ Theorem gives In triangle ACD ? ? ? ? So? ? ? ? A ? ? ? ? ? ? ? B Unit 34 34.3 Sine, Cosine and Tangent For a right angled triangle, the sine, cosine and tangent of the angle θ are defined as: Example 1 For the triangle and angle θ state which side is (a) Hypotenuse (b) Adjacent (c) Opposite ? CB ? AC AB ? Example 2 For the triangle below, what is the value of ? (a) ? ? ? (b) ? ? (c) ? ? ? Unit 34 34.4 Finding the Lengths of sides in Right Angled Triangles Example 1 Find the length of the side marked x in the triangle. Solution So ? ? ? ? ? (to 1 d. p.) Example 2 Find the length of the side marked x in the triangle Solution So ? ? ? ? ? (to 1 d. p.) 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) ? ? ? ? ?