using similarity, we know that the triangles made by the legs are similar/proportional to each other
this means
x/78 = 50/88
we can move 78 to the other side to find the value of x
x = (50/88)(78)
x = 44.3181818182
x ≈ 44.32 cm (2dp)
so the height should be 44.32 cm