Answer:
The actual height of the tree is 19.25 ft.
Explanation:
To determine the height of the tree, we can use the principle of similar triangle;
Let;
St and Sm represent the length of the shadow of the tree and the tree trimmer respectively.
And
Ht and Hm represent the actual height of the tree and the tree trimmer respectively;
Since the two triangles are similar;
[tex]\begin{gathered} \frac{Ht}{St}=\frac{Hm}{Sm} \\ Ht=\frac{Hm\times St}{Sm} \end{gathered}[/tex]Given;
Hm = 5.5 ft
St = 21 ft
Sm = 6 ft
Substituting the given values we have;
[tex]\begin{gathered} Ht=\frac{5.5\times21}{6} \\ Ht=\frac{115.5}{6} \\ Ht=19.25\text{ ft} \end{gathered}[/tex]The actual height of the tree is 19.25 ft.
