Trigonometric Ratios: sine, cosine and tangent

Given the right triangle $ABC$, we define the sine, the cosine and the tangent of an angle $x$ as:

$\sin(x)$: the sine of the angle $x$ is the ratio between the opposite cathetus and the hypotenuse: $$\sin(x)=\dfrac{a}{c} $$
$\cos(x)$: the cosine is the ratio between the adjoining cathetus and the hypotenuse: $$\cos(x)=\dfrac{b}{c} $$
$\tan(x)$: the tangent is defined as the ratio between the opposite cathetus and the adjoining one: $$\tan(x)=\dfrac{a}{b} $$