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13.391 ft
The schematic diagram of the given question is shown below;
The height of the tree is expressed as:
H = h +5
Determine the value of h using the SOH CAH TOA identity
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan40^0=\frac{h}{10} \\ h=10tan40 \\ h=10(0.8391) \\ h=8.391ft \\ \end{gathered}[/tex]Determine the height of the tree
[tex]\begin{gathered} H=h+5 \\ H=8.391+5 \\ H=13.391ft \end{gathered}[/tex]Hence the height of the tree is 13.391ft
