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