Right-Angled Triangles: Identifying Sides and Setting Up Ratios
Learn to identify opposite, adjacent and hypotenuse in right-angled triangles for IB MYP Maths Year 5. Master side labelling before applying trig ratios.
Why Side Labels Matter
Before you can use any trigonometric ratio, you need to correctly identify the three sides of a right-angled triangle relative to the angle you are working with. Getting this wrong is the single most common reason students lose marks in MYP trig questions.
The Three Sides
- Hypotenuse: Always the longest side; always opposite the right angle (90°). It does not depend on which angle you choose.
- Opposite: The side directly across from your chosen angle — it does not touch that angle.
- Adjacent: The side next to your chosen angle that is not the hypotenuse.
Key Point
Opposite and adjacent swap depending on which angle you select. Always mark your reference angle first, then label the other two sides.
Setting Up Trig Ratios
Once sides are labelled, you choose the correct ratio (sin, cos, or tan) based on which two sides are involved. This page focuses on the labelling step — trig ratios are covered in the next topics.
Common Mistakes
- Labelling adjacent as opposite when the triangle is drawn at an unfamiliar angle
- Treating the hypotenuse as the opposite side in an isosceles-looking triangle
- Forgetting to re-label sides when the reference angle changes within the same problem
How to Practise
Draw at least five right-angled triangles in different orientations. For each, pick a different reference angle and label all three sides. Check that your hypotenuse is always the longest side opposite the right angle.