A tall tree; which is situated close to the point A on a site; must be retained. You have been asked to calculate the height of a tree you position a theodolite 45m from its base. The observed angle of elevation to the top of the tree is 21 degrees, 37', 12". Given that the instrument is 1.5m off the ground, calculate the height of the tree.
+26387 A tall tree; which is situated close to the point A on a site; must be retained. You have been asked to calculate the height of a tree you position a theodolite 45m from its base. The observed angle of elevation to the top of the tree is 21 degrees, 37', 12". Given that the instrument is 1.5m off the ground, calculate the height of the tree.
\(\begin{array}{|rcll|} \hline \text{The height of the tree } &=& 1.5\ m + 45\ m \cdot \tan(21^{\circ}\ 37'\ 12 ") \\ &=& 1.5\ m + 45\ m \cdot \tan(21+\frac{37+\frac{12}{60}}{60 }) \\ &=& 1.5\ m + 45\ m \cdot \tan(21.62^{\circ} ) \\ &=& 1.5\ m + 45\ m \cdot 0.39633184969 \\ &=& 1.5\ m +17.8349332359\ m \\ &=& 19.3349332359\ m \\ \hline \end{array}\)
The height of the tree is 19.335 m
