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## Chapter 13

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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 otherangles • 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)