The question involves geometry, specifically on congruent triangles, proportions, and the Pythagorean theorem, which are fundamental concepts used to solve geometric problems including the one described where congruent triangles are used to deduce lengths based on the properties of these shapes.
The student's question falls under the category of Mathematics, specifically within the domain of Geometry, as it pertains to congruent triangles.
In the context of Geometry, congruent triangles are triangles that are identical in shape and size but may be mirrored or rotated.
These triangles have exactly the same three sides and the same three angles.
The fact mentioned that the width of the Moon as seen from point H is represented by KD = x and the angle KHD measures 0.5 degrees establishes a geometric scenario.
By extending the line AD = R to point F and drawing congruent triangles HKD and KFD, we apply the concept that congruent triangles have corresponding congruent angles and sides.
This leads to the conclusion that AC = 3R through the property of proportions which states that the ratio between certain lengths in similar triangles is constant.
Consequently, AB can also be determined as 3x using these proportions.
The information also makes reference to the Pythagorean theorem, a fundamental principle in Geometry that relates the lengths of the sides of a right triangle, which is given by the relationship a² + b² = c².
Thus, congruent triangles, proportions, and the Pythagorean theorem are crucial tools in solving various geometric problems.