Lesson 6: Solving practical problems involving trigonometric ratios
Learning Goals
Lesson Aims
Solve a variety of practical problems involving trigonometric ratios in right-angled triangles.
Learning Intentions
- Students learn to interpret practical problems, and illustrate appropriate diagrams to represent information given in questions
- Students solve real-world application problems
- Students solve higher-order thinking problems involving trigonometric ratios
Success Criteria
- Students are able to translate worded problems appropriately according to the information given by the problem.
- Students are able to use appropriate trigonometric ratios to solve for unknown sides or angles.
Syllabus Links
MAO-WM-01
- develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MA5-TRG-C-01
- Applies trigonometric ratios to solve right-angled triangle problems
Content descriptor
- Solve a variety of practical problems involving trigonometric ratios in right-angled triangles
ICT and LIT
ICT
None in this lesson
LIT
- Translate worded real-world problems into diagrams and sentences.
- Explain choice of trigonometric ratio and solution method in writing.
Prerequisite Knowledge
- Students should be able to use trigonometric ratios to solve for unknown sides and angles
- Students should be able to identify trigonometric ratios sine, cosine and tangent in terms of sides Opposite, Adjacent, Hypotenuse for a given angle
- Students should be able to solve linear equations of up to 2 steps and quadratic equations of the form $ax^2 = c$ (MA4-EQU-C-01)
Resources
Whiteboard/Smartboard (markers), student worksheet 6, calculators, Presentation slides 6
Vocabulary List
- Real-world application – using mathematics to solve problems from everyday life or practical situations
- Illustrate a diagram – draw a picture or sketch to represent information in a problem
- Interpret a problem – understand what the problem is asking and translate words into mathematics
- Angle of elevation – the angle formed when looking upward from the horizontal
- Angle of depression – the angle formed when looking downward from the horizontal
- Shadow length – the distance from the base of an object to the tip of its shadow on the ground
- Ladder problem – a common trigonometry application where a ladder leans against a wall forming a right triangle
- Solve for an unknown – find the value of an unknown side or angle
- Higher-order problem – a problem that requires more than direct substitution (may require multiple steps or reasoning)
Lesson Structure
Introduction
15 minutes
- Greet and settle students down
- Give time for students to prepare for the lesson
- This includes giving time to take out resources for the lesson
- Introduction to application of right-angled triangles
- It will be good for students to know and understand that right-angled triangles are used in various contexts because they are efficient in distributing force across its sides, making it durable and stable.
- Problem Interpretation Writing (LIT): Students write sentences describing a real-world problem and how to model it as a triangle.
Body 1
Concept teaching
10 minutes
- Examples of right-angled triangles in real life (slide 2)
- Vertical wall/building, and horizontal ground
- An object and its shadow on flat ground
- A ladder leaning against a vertical wall
- A person looking up straight to an object at an angle
- For each of the examples in (1), provide a diagram and explain how it forms a right-angled triangle (slides 3, 4, 5, 6)
Body 2
Guided practice
15 minutes
- Example Questions (slides 7, 8, 9)
- Make sure examples show a variety of examples of different situations and different applications of trigonometric ratios
- Solution Justification Writing (LIT): Students write which ratio they used and why, with supporting sentences.
Body 3
Independent practice
15 minutes
- Students work independently on worksheet 6.
Students are expected to complete the exercise for homework if they have not finished in class
Teacher roams around the classroom to help individually students with questions.
- If many require explanation on a specific question, teacher brings attention from whole class to solve together the question on the board
Conclusion
5 minutes
Learning checklist
Provide a checklist of all learning throughout the topic so far, and students tick whichever learning outcomes they are able to do.