ENTS,

   Problem #2 is attached. It is a problem of great practical significance. It involves computing the horizontal offset distance of the crown point from the trunk. As many Ents will recognize from our many discussions, the horizontal offset distance is the source of many tangent-based calculations of tree height. With laser and clinometer, we can calculate this distance quite easily. The problem calls for a derivation of the formulas needed to compute the horizontal offset. The diagram included in the attachment should make the problem clear.

Bob

Problem#2:     In the diagram below (not drawn to scale), derive a formula for computing the distance d₂ if we know S, A, and D. In practical applications, S and D are measured with a laser and A with a clinometer. The distance d₂ is called the horizontal offset as seen from the measurer’s position. Viewed from the trunk, it is the horizontal extension or how far away horizontally from the trunk the crown point is. The quantity d₂ will be recognized as the source of error for many tangent-based calculations of tree height.

Example:

 If S = 120 ft, A = 30 degrees, and D = 118 feet, then by the above formulas,

= 103.9

 feet.