Trigonometric Ratios in Right Triangle
Given a right triangle ABC.
$\sin A = \frac{\text{opposite side}}{\text{hypotenuse}}$
$\cos A = \frac{\text{adjacent side}}{\text{hypotenuse}}$
$\tan A = \frac{\text{opposite side}}{\text{adjacent side}}$
$\cot A = \frac{\text{adjacent side}}{\text{opposite side}}$
We can conclude that
$\tan A = \frac{1}{\cot A}$
Samples
$\sin A = \frac{a}{c} = \frac{7}{25}$
$\sin B = \frac{b}{c} = \frac{24}{25}$
$\cos A = \frac{b}{c} = \frac{24}{25}$
$\cos B = \frac{a}{c} = \frac{7}{25}$
$\tan A = \frac{a}{b} = \frac{7}{24}$
$\tan B = \frac{b}{a} = \frac{24}{7}$
$\cot A = \frac{b}{a} = \frac{24}{7}$
$\cot B = \frac{a}{b} = \frac{7}{24}$
$a = c\cdot\sin A$
$a = c \cdot \cos B$
$a = b \cdot \tan A$
$a = b \cdot \cot B$
$b = c\cdot\sin B$
$b = c \cdot \cos A$
$b = a \cdot \tan B$
$b = a \cdot \cot A$
Practice