Trigonometric Ratios: Finding Missing Sides with Sin, Cos and Tan
Learn sin, cos and tan definitions and how to find missing sides in right-angled triangles. MYP Maths Year 5 Standard trigonometry with SOH CAH TOA.
Defining the Three Ratios
Trigonometric ratios connect an angle in a right-angled triangle to the ratio of two of its sides. The three core ratios are:
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
- tan θ = opposite / adjacent
Many students remember these using the mnemonic SOH CAH TOA.
Choosing the Right Ratio
Identify which two sides are involved in your problem — the one you know and the one you want to find — then select the ratio that links those two sides. If you know the opposite and want the hypotenuse, use sin. If you know the adjacent and want the opposite, use tan.
Finding a Missing Side: Worked Process
- Label the triangle sides relative to the given angle.
- Write the ratio equation with the unknown on one side.
- Multiply or divide to isolate the unknown.
- Use your calculator and round to an appropriate degree of accuracy.
MYP Question Style
Questions in Criterion A and Criterion C may ask you to find a side length within an applied scenario — for example, the height of a flagpole or the width of a river. Always state the ratio you are using and show the substitution step clearly.
Common Mistakes
- Swapping opposite and adjacent because the triangle is oriented unusually
- Using the wrong ratio (e.g. sin instead of cos) after correctly labelling sides
- Not rearranging correctly when the unknown is in the denominator