Problem 1 and 2 both are on triangular laminar resting with a side on HP and the surface of the lamina is inclined to HP. There is only difference In the third position. In Problem No. 1, the resting side is inclined to HP. As the resting side is in true length in the second top view, so no need of finding beta angle.
However, in problem no. 2, one of the median is inclined to VP. As the median in the second top view is in apparent length, we need to find apparent inclination(beta angle) in the third position. Hence, beta angle has been obtained and the second top view rotated such that the median is inclined to VP by the apparent inclination(beta angle).