Question

F 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, what is the height of the tree (to the nearest tenth of a foot)?
A) 14.0 feet
B) 16.9 feet
C) 19.3 feet
D) 20.7 feet

Answer 1

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;

$tan \ \theta=\frac{opp}{adj}$

Substituting the values, we get;

$tan \ 34^{\circ}=\frac{h}{25}$

Multiplying both sides by 25, we have;

$tan \ 34^{\circ} \times 25=h$

 $0.6745 \times 25=h$

       $16.8625=h$

Rounding off to the nearest tenth of a foot, we get;

$16.9=h$

Thus, the height of the tree is 16.9 feet.

Hence, Option B is the correct answer.