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)
