From the graph, the height of the tree shows a curvilinear relationship. This can be interpreted as the tree grows taller, the trunk of the tree must grow wider.
In animals, the strength of a supporting bone is related to the cross-sectional area of the bone. This results in different proportions for legs of heavy animals. A similar trend occurs for heavier trees, as the weight increases the diameter of the tree increases where the height of the tree begins to level off.
If the strength of a tree trunk is proportional to it's cross sectional area, and the weight of a tree is related to it's volume, then the tree heights between 1000 and 3000 cm should yield a straight line on the graph for corresponding diameters.
Using the tangent to find the height of the tree was necessary for this project because we had measured or found the two other necessary components for the equation, the opposite and adjacent were already in hand. Sine would be used to find the distance to the tree base, which was known, and Cosine could be used to find the angle to the top of the tree.
On my campus, other factors than the age of the tree affecting the height and diameter are the number of other trees in the location, if canopies of trees have already grown above the new tree, it's growth will be stunted. The diameter will be affected by nutrients in the soil as well as closeness to other trees. The most affecting factor noticed was the tree canopies overlapping smaller trees. Although some of the shorter trees were more thick, if the canopy had already reached a greater height the shorter tree would have stunted height growth.
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