Naming the ratios
A ladder rests against a wall. The ladder and the ground make an angle. Call it A.
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- A right triangle ABC. The right angle is at C.
- Mark angle A with a small arc.
- Across from the right angle: the hypotenuse.
- Facing A: the opposite side.
- Beside A, but not the hypotenuse: the adjacent side.
- From B, opposite and adjacent swap.
Name the sides
The hypotenuse is the side across from the right angle. It is the longest side.
The opposite side faces angle A. The adjacent side touches A. The adjacent side is not the hypotenuse.
Opposite and adjacent depend on which angle you look from.
Three ratios
A ratio divides one side by another. Each of these three has a name.
Here A is an acute angle, one less than 90°. Each side name stands for that side's length.
Rule: In a right triangle, for acute A: sin A = opposite ÷ hypotenuse. cos A = adjacent ÷ hypotenuse. tan A = opposite ÷ adjacent.
Sin is short for sine. Cos is short for cosine. Tan is short for tangent.
| Name | Written | Division | Value |
|---|---|---|---|
| sine | sin A | opposite ÷ hypotenuse | 4/5 |
| cosine | cos A | adjacent ÷ hypotenuse | 3/5 |
| tangent | tan A | opposite ÷ adjacent | 4/3 |
At the ladder's foot, the wall side is opposite A: 4 m. The ground side is adjacent: 3 m. The ladder is the hypotenuse: 5 m.
A ratio has no unit. The metres cancel when you divide.