The AA similarity postulate states that two triangles are similar if they have 2 congruent angles. Looking at the image we can see that we have 2 lengths and one angle, but the AA similarity postulate states that we need 2 angles, then no, we cannot use AA similarity postulate to prove that they are similar. because there is only one known angle measure.
So what can we use to prove that the triangle is similar? Here, we can use SAS (side, angle, side). Anyway, the final answer is: No, because there is only one known angle measure.