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: