Answer
The height of the tree is \[29\text{ feet}\].
Work Step by Step
The side opposite to \[\text{angle }40{}^\circ \] is the height of the tree that is denoted as \[h\]. The side adjacent to \[\text{angle }40{}^\circ \] is\[35\text{ ft}\].
Compute the height of the tree using the trigonometric function of tangent as follows:
\[\begin{align}
& \text{Tan}\theta =\tfrac{\text{Side opposite to angle}\theta }{\text{Side adjacent to angle}\theta } \\
& \text{Tan}40{}^\circ =\tfrac{h}{35}\text{ } \\
& 0.839=\tfrac{h}{35}
\end{align}\]
On multiplying both sides by \[35\], we get
\[\begin{align}
& h=0.839\times 35\text{ ft} \\
& =29\text{ ft}
\end{align}\]
Hence, the height of the tree is \[29\text{ ft}\].
