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Chapter 13 Right Triangle Trigonometry §13.1 – Trigonometric Ratios • Angle – Initial side – Terminal side – Vertex §13.1 – Trigonometric Ratios •Measurement Tools - Protractor §13.1 – Trigonometric Ratios • Types of angles – Obtuse • Greater than 90° – Acute • Less than 90° – Right • Exactly 90° §13.1 – Trigonometric Ratios • Pythagorean Theorem (Right triangles) c2 = a2 + b2 §13.1 – Trigonometric Ratios • Ex: Find c in the diagram below §13.1 – Trigonometric Ratios • Ex: Find a in the diagram below §13.1 – Trigonometric Ratios • Trigonometric ratios – Relationship between an acute angle of a right triangle and the lengths of its sides • sin A = side opposite A hypotenuse • cos A = side adjacent to A hypotenuse • tan A = side opposite A side adjacent to A §13.1 – Trigonometric Ratios • Ex: Find the 3 trigonometric ratios for A §13.1 – Trigonometric Ratios • Trigonometric ratios of the other angles – Use a calculator • Examples: – Finding the trig value given the angle • Find sin 48° • Find tan 37.25° – Finding the angle given the trig value • Find if cos = 0.5402 • Find if tan = 3.421 §13.2 – Using Trigonometric Ratios to Find Angles • Finding the angles of a right-triangle – Must be given two sides – Must decide which trig ratio to use – Problems 13.2 #2, 4, 6 (p. 438) §13.3 – Using Trigonometric Ratios to Find Sides • Finding the sides of a right-triangle – Must be given one sides and one acute angle – Must decide which trig ratio to use – Problems 13.3 #2, 4, 6 (p. 440) §13.4 – Solving Right Triangles • Solving a triangle – Finding unknown values of sides or angles • Tools needed to solve triangles – Pythagorean theorem – Complementary angles add to 90° – Trigonometric ratios – Problems 13.4 #2, 4, 6 (p. 442) §13.5 – Applications Involving Trigonometric Ratios • Problem solving approach – Read through problem to be sure you understand what is being asked – Draw a diagram to help visualize the situation – Look for right triangles – Apply trigonometric concepts to solve the problem • Problems 13.5 #4, 8 (p. 445)
