Page 2: Advanced Trigonometric Applications

This page explores more complex scenarios involving multiple angles and moving objects. The content covers three distinct problem types involving statues, boats, and rockets.

Example: A statue problem using both angles of elevation and depression to calculate total height.

Example: A cliff problem calculating distance between boats using angles of depression.

Example: A rocket launch problem determining distance and speed using changing angles of elevation.

Highlight: The problems demonstrate how to:

• Calculate heights using multiple angles
• Find distances between objects using angles of depression
• Determine speed and distance using changing angles

Page 3: Navigation and Bearing Problems

This page focuses on practical applications of trigonometry in maritime navigation, introducing concepts of bearings and course calculations.

Vocabulary: Bearing - the direction of an object or course of travel, measured in degrees clockwise from true north.

Example: A boat traveling at 30 knots changes course from 200° to 290°, requiring calculations of final position and bearing.

Highlight: The solution involves:

• Vector addition for different course segments
• Pythagorean theorem for distance calculations
• Inverse tangent for bearing determination

Page 1: Basic Trigonometric Problem Solving

This page introduces fundamental concepts of solving trigonometric word problems using angles of elevation and depression. The content focuses on calculating building heights using trigonometric ratios.

Example: A 6'2" tall man looks up at a 37° angle to the top of a building from 689 inches away. The solution demonstrates converting measurements to consistent units and using tangent ratios to find the building's height.

Vocabulary: Angle of elevation - the angle formed between the horizontal plane and the line of sight looking upward.

Vocabulary: Angle of depression - the angle formed between the horizontal plane and the line of sight looking downward.

Highlight: The solution process involves:

1. Converting all measurements to the same unit (feet)
2. Using the tangent ratio to find the vertical height
3. Adding the observer's height to the calculated height