Trigonometry Solves Real-World Problems
Grade 11 Mathematics IB Analysis and Approaches SL 90-minute lesson on practical applications
Learning Objectives
Identify appropriate trigonometric ratios for real-world problems Set up and solve word problems using sine, cosine, and tangent Interpret solutions within practical contexts Communicate mathematical reasoning clearly
Trigonometric Ratios Review
SOH: Sine = Opposite ÷ Hypotenuse CAH: Cosine = Adjacent ÷ Hypotenuse TOA: Tangent = Opposite ÷ Adjacent Choose the ratio based on known and unknown values
Worked Example: The Ladder Problem
A ladder leans against a wall at 60° to the ground The base is 5 feet from the wall Find the height where the ladder touches the wall Which ratio should we use and why?
Real-World Applications
{"left":"Architecture: Calculating roof angles and building heights\nNavigation: Finding distances and bearings at sea\nEngineering: Designing ramps and bridges","right":"Astronomy: Measuring distances to celestial objects\nSports: Analyzing projectile motion in athletics\nSurveying: Mapping terrain and property boundaries"}
Group Challenge: Canyon Depth
You stand 100 meters from a canyon edge The angle of depression to the canyon floor is 35° Calculate the approximate depth of the canyon Work in groups of 4-5 students
Quick Check: Problem-Solving Strategy
What are the essential steps for solving trigonometry word problems? How do you decide which trigonometric ratio to use? Why is drawing a diagram important?
Key Takeaways & Next Steps
Trigonometry solves practical problems in many careers Always start with a clear, labeled diagram Choose ratios based on known vs. unknown sides/angles Check that your answers make sense in context Next: Law of Sines and Cosines for non-right triangles