SOH
sin ฮธ = Opposite รท Hypotenuse
๐ฏ Learning Objectives
- state sine, cosine and tangent ratios;
- connect each ratio to the correct side pair;
- select a ratio from known and unknown information;
- avoid memorising without understanding.
Introduction
This lesson develops SOH CAH TOA from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
SOH CAH TOA
CAH
cos ฮธ = Adjacent รท Hypotenuse
TOA
tan ฮธ = Opposite รท Adjacent
How to Choose the Ratio
Circle the side you know and the side you need.
โ
Which ratio contains exactly those two side names?
โ
Opposite + Hypotenuse โ sine
Adjacent + Hypotenuse โ cosine
Opposite + Adjacent โ tangent
Worked Examples
Reason through the method
- Identify the known information and what must be found.
- Choose the definition, property or formula that connects them.
- Substitute carefully and show each step.
- Check the notation, units and whether the result is sensible.
Practice Questions
- Which ratio uses opposite and hypotenuse?
- Which ratio uses adjacent and hypotenuse?
- Which ratio uses opposite and adjacent?
- You know the hypotenuse and need the adjacent side. Choose the ratio.
- You know the opposite and need the adjacent side. Choose the ratio.
โ Check Your Work
Show answers and working
- Sine.
- Cosine.
- Tangent.
- Cosine, because it contains adjacent and hypotenuse.
- Tangent, because it contains opposite and adjacent.
๐งญ Interactive Lab: SOH CAH TOA Side Highlighter
Change the values or make a choice and watch the mathematics respond.
Choose a ratio.
Summary
๐ Remember
- Label the triangle before choosing a formula.
- Use degree mode unless the question says otherwise.
- Keep full calculator values until the final rounding step.
โ ๏ธ Common Mistakes
- Using the wrong reference angle.
- Rounding too early.
- Forgetting units or the degree symbol.
โญ Exam Tips
- Write the formula before substituting.
- Sketch and label any diagram that is not already provided.
- Check whether the answer is sensible for the shape.
๐ Did You Know?
Surveyors, engineers, pilots and architects use trigonometry to calculate distances that are difficult or unsafe to measure directly.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.