Chapter 13 Download

Transcript
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)