Final answer:
The question involves applying trigonometry and geometry to find dimensions and properties of triangles based on given angles and side lengths in a high school-level mathematics context.
Step-by-step explanation:
The student's question is related to trigonometry and geometry, specifically to the concept of similar triangles and angular measurements. Given the angle ∠K and the lengths of sides q and k, the task seems to be about finding certain dimensions or properties of other triangles that are in some relation to the given triangle, using congruence and proportions. This kind of problem is typically encountered in high school mathematics, particularly in a course that covers geometry or pre-calculus topics.