SOH-COH-TOA: Trigonometric Ratios Mastery
Year 10 Mathematics Understanding Sine, Cosine, and Tangent 60-minute lesson
National Curriculum Connections
Geometry and Measures (KS4 - Year 10) Standard conventions for labelling triangle sides Apply trigonometric ratios to find angles and lengths Reasoning and problem-solving with right-angled triangles
Learning Objectives
Understand sine, cosine, and tangent as ratios Correctly identify opposite, adjacent, and hypotenuse sides Use SOH-COH-TOA to calculate lengths and angles Build confidence through practical activities
Starter Activity: Triangle Side Detective
Look at the right-angled triangle on your worksheet Label the sides: hypotenuse, opposite, adjacent Remember: hypotenuse is always the longest side Use angle θ (theta) as your reference point
Meet SOH-COH-TOA
SOH: Sine = Opposite ÷ Hypotenuse COH: Cosine = Adjacent ÷ Hypotenuse TOA: Tangent = Opposite ÷ Adjacent Memory trick: 'Some Old Hippie Caught Another Hippie Tripping On Acid'
Triangle Ratios Visualized
Worked Example: The 3-4-5 Triangle
Triangle with sides: opposite = 3cm, adjacent = 4cm, hypotenuse = 5cm Sin θ = 3/5 = 0.6 Cos θ = 4/5 = 0.8 Tan θ = 3/4 = 0.75
Guided Practice: Your Turn!
Question 1: Find sin θ when opposite = 6cm, hypotenuse = 10cm Question 2: Find cos θ when adjacent = 8cm, hypotenuse = 10cm Question 3: Find tan θ when opposite = 6cm, adjacent = 8cm Work in pairs and use mini whiteboards
Triangle Detective Challenge
Receive your detective cards with mystery triangles Use SOH-COH-TOA to find missing sides or angles Show your working clearly Discuss your method with a partner before writing
Quick Check: Which Ratio?
If I want to find the angle and I know the opposite and adjacent sides, which ratio do I use? If I know the hypotenuse and need to find the opposite side, which ratio helps? What's the first step when solving any triangle problem?
Homework: Practice Makes Perfect
5 practice problems using SOH-COH-TOA Include both finding ratios and using inverse functions Challenge question: real-world application Show all working clearly
Lesson Summary & Next Steps
SOH-COH-TOA helps us find missing sides and angles Always identify triangle sides first Practice builds confidence and accuracy Next lesson: Using calculators for inverse trigonometric functions