If tan(alpha)=f, and f²=y²+x², and tan(alpha)=y/x then y²+x²=tan²(alpha)=y²/x².

y²x²+x⁴=y²

y²(x²-1)=-x⁴

y²=x⁴/(-x²+1)

Assuming y and x are real-valued and positive, this means x² must be between 0 and 1 (and therefore x is, as well), but there are no particular constraints, beyond that. y is a function of x, and it's one-to-one for 0<x<1, so as your triangle gets taller, the x side must get closer and closer to 1, asymptotically.