Final answer:
To find the measure of ∠ABC, if it is confirmed to be a right angle, the measure is 90 degrees. To determine the value of x, additional information is required. Vector component analysis using trigonometric functions is necessary for this type of problem.
Step-by-step explanation:
The student's question pertains to finding the value of x and the measure of ∠ABC in the context of a right-angle triangle and vectors.
The question presents a scenario involving the width of the Moon as seen from a point H and a series of geometric relations that result in the determination that AC = 3R and AB = 3x.
Additionally, vector components are mentioned as a method for analyzing the properties of vectors within a right triangle context.
To find the magnitude and components of a vector, equations involving cosine and sine functions are used due to the right-angle relationships.
For this problem, it seems that more specific information or a diagram is required to provide a step-by-step solution. However, to find the measure of ∠ABC, if it is a right angle, it is definitively 90 degrees.
To determine the value of x, more information about the triangle or the vectors' magnitudes and angles is necessary. The use of cosine and sine functions with respect to the given angles is a key part of determining the vector components for solving such a problem.