Final answer:
Engineering mechanics involve analyzing structures and determining reaction forces. With horizontal components provided, we found Bx to be 15.4 kips. Without further vertical force details, Ay cannot be calculated but should be upward for equilibrium if the only other vertical force is downwards.
Step-by-step explanation:
The question pertains to statics in engineering mechanics, specifically analyzing a structure to determine the reaction forces at supports A and B. Given the information, if Ax (horizontal component at A) is 49.8 kips and Rx (the sum of horizontal forces which equals Ax + Bx) is 65.2 kips, we can find Bx by subtracting Ax from Rx, yielding Bx = 15.4 kips. The direction of Ax will be horizontal since it's a component of a vector.
For the vertical components, if an object is at rest (in equilibrium), the sum of forces acting on it must be zero. Therefore, if force X acts downward with a magnitude of x, then By must act upward with an equal magnitude of x as well, to satisfy equilibrium conditions in the vertical direction.
The resultant R's magnitude given is 81.2 kips, but without additional vertical forces information, we cannot specifically calculate Ay. However, equilibrium dictates that the sum of upward- and downward-acting vertical forces should be equal, with Ay being upward if the only other vertical force is downward.