area
$$ A = \frac{a b}{2} = \frac{c h_c}{2} $$
perimeter
$$ P = a + b + c $$
Pythagorean theorem
$$ c^2 = a^2 + b^2 $$
height to edge c
$$ h_c = a \cdot\sin\beta = b \cdot\sin\alpha $$
angle
$$ \alpha + \beta = 90^\circ $$
trigonometric functions
$$
\begin{aligned}
\sin\alpha &= \frac{a}{c} \\ \\
\cos\alpha &= \frac{b}{c} \\ \\
\tan\alpha &= \frac{a}{b} \\ \\
\cot\alpha &= \frac{b}{a}
\end{aligned}
$$
$$
\begin{aligned}
a^2 &= c \cdot c_a \\ \\
b^2 &= c \cdot c_b \\ \\
h_c^2 &= c_a \cdot c_b
\end{aligned}
$$
