The height is the perpendicular distance from a point to the opposite side.
triangle
a, b, c
edge
ha
height to edge a
hb
height to edge b
hc
height to edge c
α, β, γ
angle
Calculator
Formulas
triangle
area
$$ A = \frac{a h_a}{2} = \frac{b h_b}{2} = \frac{c h_c}{2} $$
perimeter
$$ P = a + b + c $$
height
$$
\begin{aligned}
h_a &= b \cdot\sin\gamma = c \cdot\sin\beta \\ \\
h_b &= a \cdot\sin\gamma = c \cdot\sin\alpha \\ \\
h_c &= a \cdot\sin\beta = b \cdot\sin\alpha
\end{aligned}
$$
$$
\begin{aligned}
a &= \sqrt{b^2 + c^2 - 2 \cdot b c \cdot\cos\alpha} \\ \\
b &= \sqrt{a^2 + c^2 - 2 \cdot a c \cdot\cos\beta} \\ \\
c &= \sqrt{a^2 + b^2 - 2 \cdot a b \cdot\cos\gamma}
\end{aligned}
$$
