My 25 followers problem

Geometry Level 4

A man walks along a straight road and observes that the greatest angle subtended by two objects is \(\alpha\); from the point where this greatest angle is subtended he walks a distance \(c\) along the road, and finds that the two objects are now in a straight line which makes an angle \(\beta\) with the road.

Find the distance between the two objects upto three decimal places.

Details and assumptions:

  • \(\alpha=60^\circ\)
  • \(\beta=30^\circ\)
  • \(c=3+\sqrt{3}\)

Hint: Generalise, then specialise.

This problem is not original and has been taken from a book by S. L. Loney.

This problem is part of my set: Geometry


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