Final answer:
The question requires more specific information regarding each mathematical problem, such as side lengths or angles for geometry questions and known quantities for physics-related dimensions. Without additional details, it is not possible to provide the exact lengths or measures sought in the inquiry.
Step-by-step explanation:
Your question appears to have multiple parts and seems to be focusing on subjects relating to geometry, trigonometry, and basic physics dimensions. However, it's not clear which specific problem you're asking about as there are references to sides of triangles, arc length, cube dimensions, and coordinates in three-dimensional space.
For example, to find the length of side PR in triangle PQR, we would need more information such as the lengths of the other sides or the angles involved. Similarly, for the measure of angle J in triangle JKL, additional data are required unless it is a special triangle (like a right triangle or an equilateral triangle).
Regarding the array, if you are looking to find the area to express the size of an array, you would calculate the product of its length and width. If it's a square array, then all sides would be equal, and the area would be the side length squared.
For the problems related to physics and dimensions, such as the one about cube side length with a given mass and density, you would use the density formula Density = Mass/Volume to solve for the cube's side length. Remember that the volume of a cube is side length cubed.