Labelling Sides of a Right-Angled Triangle

Name the hypotenuse, opposite and adjacent sides of a right-angled triangle from the marked angle, see how the labels swap when the angle changes, and match each pair of sides to sin, cos or tan.

اقرأ هذا الدرس مشروحاً بالعربي ←

Three Sides, Three Names

In a right-angled triangle each side has a name. Two names depend on which angle you are working from.

Side	How to spot it
Hypotenuse	the longest side, across from the right angle
Opposite	across from the marked angle
Adjacent	next to the marked angle, not the hypotenuse

Key idea

Always find the hypotenuse first. It is the one side that never changes name.

Name the Sides From the Angle

Triangle $A B C$ has its right angle at $B$ . The marked angle is $3 5^{\circ}$ at $A$ .

Worked example

1
$hyp = A C$ — The hypotenuse is across from the right angle. The right angle is at $B$ , so the side facing it is $A C$ .
2
$opp = B C$ — Stand at the marked angle $A$ and look across the triangle. The side you face is $B C$ , so it is the opposite.
3
$adj = A B$ — Two sides touch $A$ : $A C$ and $A B$ . $A C$ is already the hypotenuse, so the one left, $A B$ , is the adjacent.

Common mistake

Calling the hypotenuse the adjacent. It touches the angle too, but it is always the hypotenuse.

Change the Angle, Swap the Labels

The 1-mark question often marks the other acute angle. Same triangle, but now the marked angle is $5 5^{\circ}$ at $C$ .

Worked example

1
$hyp = A C$ — The right angle has not moved, so the side across from it is still $A C$ . The hypotenuse never changes.
2
$opp = A B$ — Stand at the new marked angle $C$ and look across the triangle. The side you face is $A B$ , so it is the opposite.
3
$adj = B C$ — Two sides touch $C$ : $A C$ and $B C$ . $A C$ is the hypotenuse, so $B C$ is the adjacent.

Common mistake

Keeping the old labels. Opposite and adjacent swap when the angle moves to the other corner.

Which Pair, Which Ratio

Each trig ratio uses exactly two sides. Name the two sides first, then the ratio follows.

Two sides	Ratio
opposite and hypotenuse	$sin$
adjacent and hypotenuse	$cos$
opposite and adjacent	$tan$

Memory trick

SOH CAH TOA: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.

Which Method? Read the Question

Labelling is always the first line of working.

You see	You do
Right angle marked	the side across from it is the hypotenuse
One acute angle marked	label opposite and adjacent from that angle
Two sides, no angle, find a side	Pythagoras' Theorem
An angle and a side, find another	Choosing the Right Trigonometric Ratio
30, 45 or 60 degrees, exact answer	Special Angles and Exact Ratios

Key idea

Write hyp, opp and adj on the diagram before any calculation. It stops most wrong ratios.

Practise labelling sides of a right-angled triangle now

Interactive visual aids, then real past-paper questions marked on your working like the exam. Free to start.

Practise free on Lemmara

Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education or Pearson Edexcel. The lessons and worked examples are Lemmara’s own.