Trigonometry Foundations for Year 9
Mathematics and Numeracy Curriculum for Wales 60-minute lesson for ages 13-14
What is Trigonometry?
Study of relationships between angles and sides in triangles Focuses on right-angled triangles Uses ratios to solve problems Essential for engineering, physics, and real-world applications
Learning Objectives
Define sine, cosine, and tangent ratios Identify opposite, adjacent, and hypotenuse sides Calculate unknown sides and angles Apply trigonometry to real-world problems Demonstrate clear mathematical reasoning
Triangle Sides Quiz
Look at the triangle on the board Identify the hypotenuse, opposite, and adjacent sides Hold up your colored cards when prompted Remember: angle position matters!
Naming Triangle Sides
Hypotenuse: longest side, opposite the right angle Opposite: side across from the angle we're considering Adjacent: side next to the angle we're considering The angle position determines which is which!
The Three Trigonometric Ratios
Sine (sin) = Opposite ÷ Hypotenuse Cosine (cos) = Adjacent ÷ Hypotenuse Tangent (tan) = Opposite ÷ Adjacent Remember: SOH-CAH-TOA!
Worked Example
{"left":"Given: Right triangle with 30° angle, hypotenuse = 10 cm\nFind: opposite side length\nSolution: sin(30°) = opposite ÷ hypotenuse","right":"sin(30°) = opposite ÷ 10\n0.5 = opposite ÷ 10\nopposite = 0.5 × 10 = 5 cm"}
Paired Problem Solving
Work in pairs with triangle cards Identify given information first Choose the correct trigonometric ratio Set up your equation before calculating Use scientific calculators to find answers
Real-World Applications
Calculating building heights using shadows Finding angles for wheelchair ramps Navigation and GPS systems Engineering and construction projects Astronomy and satellite positioning
Exit Question
In one sentence, explain why sine is the ratio of opposite to hypotenuse. Write your answer on a sticky note This helps me understand your learning today