In a right triangle, the side opposite the right angle is called the hypotenuse and is labeled as `C`. The other two sides are called the legs and are labeled as `A` and `B`. The angle opposite side `A` is labeled as `x`.
To find `cos(x)`, `sin(x)`, and `tan(x)` in terms of `A`, `B`, and `C`, you can use the following trigonometric formulas:
- `cos(x) = A/C`
- `sin(x) = B/C`
- `tan(x) = sin(x) / cos(x) = B/A`
So if you know the lengths of the sides `A`, `B`, and `C`, you can use these formulas to find `cos(x)`, `sin(x)`, and `tan(x)`.
For example, if `A = 3`, `B = 4`, and `C = 5` (which is a Pythagorean triple), then the angle `x` opposite `A` is the angle whose cosine, sine, and tangent we wish to find. Using the formulas above, we have:
- `cos(x) = A/C = 3/5`
- `sin(x) = B/C = 4/5`
- `tan(x) = sin(x) / cos(x) = (4/5) / (3/5) = 4/3`
Therefore, in this case, `cos(x) = 3/5`, `sin(x) = 4/5`, and `tan(x) = 4/3`.