Final answer:
Without additional data on triangle GHY, it is not possible to provide a numerical answer for the length of segment HU, which goes from the incenter U to vertex H.
Step-by-step explanation:
The student has asked for help with finding the length of segment HU where U is the incenter of triangle GHY. To solve this, one would typically use the properties of bisectors and trigonometric relationships within the triangle. However, without specific measurements or additional data, such as the lengths of sides or angles in triangle GHY, it is not possible to provide a numerical answer for HU.
Generally, in a triangle, the incenter is the point where the angle bisectors of each corner meet. This point is equidistant from all sides of the triangle. The segment from the incenter to any side of the triangle is referred to as the inradius. Without the necessary triangle measurements though, we can't determine the length of HU.