Given:
The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.
We need to determine the height of the tree.
Height of the tree:
Let the height of the tree be h.
The height of the tree can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Substituting the values, we get;
[tex]tan \ 34^{\circ}=\frac{h}{25}[/tex]
Multiplying both sides by 25, we have;
[tex]tan \ 34^{\circ} \times 25=h[/tex]
[tex]0.6745 \times 25=h[/tex]
[tex]16.8625=h[/tex]
Rounding off to the nearest tenth of a foot, we get;
[tex]16.9=h[/tex]
Thus, the height of the tree is 16.9 feet.
Hence, Option B is the correct answer.
