The idea, step by step
Choose the angle first
The hypotenuse faces the right angle. Relative to an acute angle θ, the opposite side is across the triangle and does not touch θ. The adjacent side touches θ but is not the hypotenuse.
Trace the two sides that touch your acute angle, then exclude the hypotenuse to find adjacent. Opposite is the remaining side.
A new reference angle changes two labels
Using the other acute angle swaps opposite and adjacent. The hypotenuse stays the same because the right angle has not changed.
Turning a picture cannot change these rules. Top, bottom, left and right describe the page, not a side’s relationship to an angle.
A common trap
The adjacent side is always horizontal.
Instead: Adjacent means touching the chosen acute angle, excluding the hypotenuse. It can have any orientation.
See the thinking
Label lengths
For the lower-right angle θ in the sketch, name the opposite, adjacent and hypotenuse lengths.
- The 5 cm side faces the right angle: hypotenuse.
- The 3 cm side does not touch θ: opposite.
- The 4 cm side touches θ and is not hypotenuse: adjacent.
Switch to the top angle
For the upper angle φ in the sketch, name the opposite, adjacent and hypotenuse lengths.
- The 5 cm hypotenuse stays fixed.
- The horizontal 4 cm side is now opposite φ.
- The vertical 3 cm side is now adjacent to φ.
Check your understanding
Triangle ABC is right-angled at B. Which side is opposite angle A?
Show answer
BC
Side BC does not touch angle A; AC is the hypotenuse and AB is adjacent.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- For θ in the sketch, name the opposite side.1 mark
- For θ in the sketch, name the adjacent side.1 mark
- For θ in the sketch, name the hypotenuse.1 mark
- Now use upper angle φ. Name its opposite and adjacent sides.2 marks
- Triangle ABC is right-angled at B. For angle A, name the hypotenuse, opposite side and adjacent side.3 marks
- A right triangle is rotated on the page. Does its hypotenuse change? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- For θ in the sketch, name the opposite side.1 mark
Side a is across from θ.
a - For θ in the sketch, name the adjacent side.1 mark
Side b touches θ and is not the hypotenuse.
b - For θ in the sketch, name the hypotenuse.1 mark
Side c faces the marked right angle.
c - Now use upper angle φ. Name its opposite and adjacent sides.2 marks
Changing the reference angle swaps the two shorter-side labels.
Opposite b; adjacent a - Triangle ABC is right-angled at B. For angle A, name the hypotenuse, opposite side and adjacent side.3 marks
AC faces the right angle B.
BC does not touch A; AB does touch A.
Hypotenuse AC; opposite BC; adjacent AB - A right triangle is rotated on the page. Does its hypotenuse change? Explain.2 marks
Rotation does not change any angle.
The same side remains opposite the right angle.
No
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Mathematics
Year 9 similarity, Pythagoras and right-triangle trigonometric ratios, with prerequisite revision. Non-right-triangle sine/cosine rules are not required.
Official curriculum source ↗