What type of casket construction uses a method that features panels at right angles to the base?

The correct answer, state construction, refers to a casket construction method where the side panels are positioned at right angles to the base. This design choice gives the casket a more traditional and formal appearance, often associated with higher-end models. In state construction, the vertical sides contribute to a stately silhouette, enhancing the overall aesthetic appeal of the casket and ensuring stability and structural integrity.

In contrast, flat-bottom construction generally features a base that is horizontal, leading to a more simplistic design, while angle construction would imply slanted or non-vertical sides, which do not align with the description provided in the question. Rounded construction typically involves a curved design that diverges significantly from the concept of right angles, resulting in a distinctly different look and structure.