We can find an acute triangle with the three altitude lengths 1, 3, and h, if and only if h^2 belongs to interval (p,q). Find (p, q).
+178 The three sides are (Letting area be K) \(\frac{2K}{3}, \frac{2K}{1}, \frac{2K}{h}\).
Then, simply do triangle inequality with cases depending on how big \(\frac{2K}{h}\) is.
