Trigonometric Ratios Review and Practice
Year 10 Mathematics SOH CAH TOA and Applications Finding Missing Lengths
Quick Check: What Do You Remember?
What does SOH CAH TOA stand for? Which ratio would you use to find an opposite side when you know the hypotenuse? How do you rearrange sin(θ) = opposite/hypotenuse to find the angle?
Rearranging Trigonometric Equations
sin(θ) = opposite/hypotenuse → θ = sin⁻¹(opposite/hypotenuse) cos(θ) = adjacent/hypotenuse → adjacent = cos(θ) × hypotenuse tan(θ) = opposite/adjacent → opposite = tan(θ) × adjacent Remember: Use inverse functions to find angles
SOH CAH TOA Reference Guide
Ratio Selection Challenge
Look at each triangle scenario Identify what information is given Choose the correct trigonometric ratio Justify your choice to a partner
When to Use Each Ratio
{"left":"SINE: When you have angle and hypotenuse, need opposite\nSINE: When you have opposite and hypotenuse, need angle\nCOSINE: When you have angle and hypotenuse, need adjacent","right":"COSINE: When you have adjacent and hypotenuse, need angle\nTANGENT: When you have angle and adjacent, need opposite\nTANGENT: When you have opposite and adjacent, need angle"}
Finding Missing Lengths: Step-by-Step
Step 1: Label the triangle (opposite, adjacent, hypotenuse) Step 2: Identify given information and what you need to find Step 3: Choose the appropriate trigonometric ratio Step 4: Substitute values and solve Step 5: Check your answer makes sense
Guided Practice: Missing Lengths
Triangle A: Find the missing side length Triangle B: Calculate the unknown measurement Triangle C: Solve for the missing dimension Show all working and check answers
Common Mistakes to Avoid
What happens if you confuse opposite and adjacent? Why is it important to check if your answer is reasonable? When might you get an error message on your calculator?
Summary and Key Takeaways
SOH CAH TOA helps choose the correct ratio Always label the triangle relative to the given angle Rearrange equations to solve for unknown values Check answers are reasonable and make sense Practice with different triangle orientations