The lengths of the sides of triangle RST are 3,4 and $\mathrm{y}$.
Find the interval of the real number and side-length $y$ corresponding to the side $RT$ such that the angle corresponding to it ($\angle RST$) in a triangle with two other sides three and four is acute without the law of cosines.
I was thinking we may draw a altitude to the side with length $y$, and then that divides into a section with length $a$ another section with length $b$ so that $a+b=y$.
Under the acute angle hypothesis I think $a^2+h^2<9, (y-a)^2+h^2<16$, but I'm not sure how to prove this is the result of having a correspondence with an acute angle or whether this preposition is relevant, and I'm not sure what to draw.