Formula Trapezoid Height Angle Side length
$$\class{green}{h} ~=~ c \, \sin(\alpha)$$ $$\class{green}{h} ~=~ c \, \sin(\alpha)$$ $$\alpha ~=~ \arcsin\left( \frac{\class{green}{h}}{c} \right)$$ $$c ~=~ \frac{\class{green}{h}}{\sin(\alpha)}$$
Height
$$ \class{green}{h} $$ Unit $$ \mathrm{m} $$ Height of the trapezoid, i.e. the distance between the sides \( a \) and \( b \).
Angle
$$ \alpha $$ Unit $$ - $$ The angle enclosed by the sides \( c\) and \( a \). Alternatively, the trapezoid height can be expressed with the angle \( \beta \). This is the angle enclosed by the sides \( d\) and \( c \):\[ h ~=~ d \, \sin(\beta) \]
Side length
$$ c $$ Unit $$ \mathrm{m} $$ Length of the corresponding side of the trapezoid (see illustration). If \( c = d \), then the trapezoid is isosceles.