Çözüldü Trigonometry

A problem with only the answer from Rutgers University: (it has slightly been changed to a metric system with the choices so that no calculator is needed.)

If a pilot in an airplane flying at 25000 meters sees two towns directly ahead of the cockpit in a straight line, and the angles of depression to the towns are 30° and 60°, how far apart are those towns in kilometers?

A) 25·√2
B) 25·√3
C) 25 / √2
D) 50 / √3
E) 50·√2

x: The distance between the towns (km)
y: The distance between the projection point of the airplane on the ground and the nearer town (km)
x + y = 25·cot(30°)....(I)
y = 25·cot(60°)....(II)
Subtracting (II) from (I) side by side x = 25·sin(60° - 30°) / [ sin(60°)·sin(30°) ] = 25 / sin(60°) = 50 / √3 km ≈ 28,9 kilometers.

Note: Drawing and simple trigonometric operations are homework for the interested students.
Original Problem: https://math.rutgers.edu/docman-lis.../course-materials/112-1/1525-m112rev-pdf/file
(Page 6, Question 31)