Logo for MightySolve
Heights in a parallelogram

The height in a parallelogram can be calculated using two different formulasha=Aaha=bsin(β) \begin{aligned} h_a &= \frac{A}{a} \\[1em] h_a &= b \sin \left( \beta \right) \end{aligned} The formulas for hbh_b are symmetric to the ones for hah_a. This means we havehb=Abhb=asin(α). \begin{aligned} h_b &= \frac{A}{b} \\[1em] h_b &= a \sin \left( \alpha \right). \end{aligned} The first of these formulas originates from the one for the area in a parallelogram and the other from using the definition of the sine in a right triangle constructed.