Discussion
In Christen hypsometer, find length bd for a tree of 24 m height when BD (staff length) is 4 m and ab (distance between the flanges) is 33 cm.
Answer: D
The length bd is 5.50 cm.
The Christen hypsometer is held so that the top A and base B of the tree line up with its two flanges a and b. The line of sight to the top D of a staff of known length BD then cuts the scale at d. By similar triangles:
\[ \begin{aligned} \frac{bd}{ab} &= \frac{BD}{AB} \\ bd &= \frac{33 \times 4}{24} \\ &= 5.5\ \text{cm} \end{aligned} \]
The scale is graduated this way: the taller the tree, the shorter bd. 2.50, 3.50 and 4.50 cm would correspond to trees of about 53, 38 and 29 m.
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