Find those angles

It is a right angled triangle. So , assuming the hypotenuse( h ) is always the longest side, we can know that h=6. To find the smallest angle , we must find the arcsin of the shortest side to h , and we found that 3 happens to be the smallest value, which is the hypotenuse. Therefore, $\arcsin \frac{o}{h}=\theta$ , plug in the numbers we get $\arcsin\frac{3}{6}=0.52359878$ , which corresponds to $30\deg$ .

Taking hypotenuse as 6 and the other two sides as 3 and 3 root 3, we find cos of the smallest angle. It results in root 3 /2 which is cos 30'

A triangle with the angles $30,60$ and $90$ has the ratio $1:\sqrt{3}:2$ for the length of its sides

We can scale up the ratio to be $1:\sqrt{3}:2 = 3:3\sqrt{3}:6$ and it satisfies the lengths given in the question

Therefore, the smallest angle in the triangle is $30$ degrees

It seems like the length given here is quite familiar, since the lengths are in the form of $2x, x, x\sqrt3$ , where $x$ is arbitrary positive real values. Therefore, this implies to the smallest angle which is $\boxed {30}$ degrees.