Chapter 13

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)