Question

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

Answer 1

The height of the tree to the nearest foot is 33 ft

Answer 2

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 $\angle F=90^{\circ}$

Thus, the triangle $\Delta PFT$ is a right triangle.

Now, we can apply the trigonometric ratio, tan in this triangle as:

$tan(\angle P)=\frac{Perpendicular}{Base} =\frac{TP}{PF}$

$\therefore tan(35^{\circ})=\frac{TF}{47}$

$TF=47\times tan(35^{\circ})\approx32.91\approx33$

Thus, the the height of the tree to the nearest foot is 33 feet.