For a better understanding of the solution provided here please go through the diagram in the attached file.
In the diagram, F is the foot of the tree.
T is the top of the tree. Then TF will be the height of the tree.
P is the point on the ground 47 feet from the foot of a tree. Therefore, PF=47.
Now, we know that the tree grows vertical from the ground and thus [tex] \angle F=90^{\circ} [/tex]
Thus, the triangle [tex] \Delta PFT [/tex] is a right triangle.
Now, we can apply the trigonometric ratio, tan in this triangle as:
[tex] tan(\angle P)=\frac{Perpendicular}{Base} =\frac{TP}{PF} [/tex]
[tex] \therefore tan(35^{\circ})=\frac{TF}{47} [/tex]
[tex] TF=47\times tan(35^{\circ})\approx32.91\approx33 [/tex]
Thus, the the height of the tree to the nearest foot is 33 feet.
