Ratio problem in geometry 


What I think is the answer is not entirely correct. I think option (E)
  should be added because of same ration. Am I right?

 A: Option (E) is not a valid answer. In (E) it is the sides that are in that ratio. The ratio of the angles is not necessarily the same as the ratio of the sides, in fact, it hardly ever is.
As an example, take a  $30^\circ-60^\circ-90^\circ$ triangle.  The angles are in the ratio $1:2:3$ but the sides are in the ratio $1:\sqrt{3}:2$.
Remarks: $1.$ The Sine Law tells us exactly the relationship between ratios of sides and ratios of angles. It says that
$$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}.$$
$2.$ We address specifically the triangle from (E) with sides $4$, $3$, and $2$, and show how to calculate the angles.
The smallest angle is opposite the smallest side. If we call that angle $A$, then by the Cosine Law we have
$$2^2=3^2+4^2-(2)(3)(4)\cos A.$$
That makes $\cos A=\frac{21}{24}$, so $A$ is about $28.955$ degrees. We could calculate the others, and show they are not in the ratio $2:3:4$. 
But we can do it with less work. The angles cannot be in the ratio $2:3:4$, since if they were, the smallest angle would be $40^\circ$.
