Right Triangle Trigonometry 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 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)