Dedicated to Ayush Rai

Geometry Level 5

A flagstaff is on the top of a tower which stands on a horizontal plane.

A person observes the angles subtended by the flagstaff and the tower at a point on the horizontal plane as \(\alpha\) and \(\beta\) respectively.

He then walks a distance \(a\) towards the tower and observes that the angle subtended by the flagstaff remains unchanged.

Enter the height of the tower correct to three decimal places.

Details and assumptions:

  • \(\alpha=15^\circ\)
  • \(\beta=30^\circ\)
  • \(a=2\)

Clarification figure:

Bonus questions:

  • Generalise for arbitrary values of \(\alpha, \beta\) and \(a\).
  • Find the height of the flagstaff in this generalised situation.

Problem Loading...

Note Loading...

Set Loading...