from a point on the ground 47 feet from the foot of a tree, the angle of evelation of the top of the tree is 35 degrees. find the height of the tree to the nearest foot

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.