Assuming that the same point of the mountain is observed, I think the question has errors and here is why. (unless of course I had misread the question)
Look at it this way:
- First of all, the angle of elevation must decrease with increasing distance, which is common sense. If you look at a tower directly above you, the angle of elevation is much more than if you look at the same point from a distance away.
- The distance between the observer and the directly north mountain, would be less than the distance between the observer and the same mountain if he or she were to move 200 metres east (or any distance away) from his starting point.
- Since the distance between the observer and mountain has increased when 200 metres east of the initial position, therefore the angle of elevation must have decreased from the original position.
- This is also proved by the right-angled triangle formed when you draw out the diagram. At the distance 200 metres east of the initial position, the hypotenuse of the right-angled triangle is formed. Since the hypotenuse is the longest side of the triangle, the distance from the mountain must have increased between the two points.
- However, the question implies that the angle of elevation has increased which is not possible in real life and since we are dealing with real numbers, the situation described by the question is not valid and hence that explains why people are getting negative numbers.
