Concept 8.1
Opposite, Adjacent, Hypotenuse
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
In △ABC right-angled at B, for the acute angle A: sin A = BC/AC (opposite/hypotenuse), cos A = AB/AC (adjacent/hypotenuse) and tan A = BC/AB (opposite/adjacent).
The intuition
'Opposite' and 'adjacent' are not fixed sides. They are named from where you stand: from angle A, the opposite side is the one A looks across at.
Switch to angle C and the same two sides swap names. So the first thing to fix is the angle; then read the sides from it.
The attention
Look at the angle first, then name the sides from it.
From angle A: sin A = BC / AC, AB is adjacent
Look hereNot here
- Look here
- The side opposite the angle. BC is opposite A because it doesn't touch A. Naming starts at the angle.
- Not here
- The side next to the angle. AB touches angle A, so it is adjacent. Calling it 'opposite' because of where it sits in the drawing gives cos A instead of sin A.
- What it teaches
- Fix your viewpoint before you name anything.