To solve this problem, we can use trigonometry. Let's denote:
ℎ
h as the height of the observer's eye level above the ground.
�
d as the distance from the observer to the base of the tower.
�
H as the height of the tower.
We have a right triangle formed by the observer's line of sight, the height of the tower, and the ground. Using the tangent function:
tan
(
3
5
∘
)
=
�
�
tan(35
∘
)=
d
H
We can rearrange this equation to solve for
�
H:
�
=
�
×
tan
(
3
5
∘
)
H=d×tan(35
∘
)
Substituting the given values,
�
=
80
d=80 meters and
tan
(
3
5
∘
)
≈
0.7002
tan(35
∘
)≈0.7002, we get:
�
≈
80
×
0.7002
≈
56.016
meters
H≈80×0.7002≈56.016 meters
Now, to find the height of the observer's eye level above the ground, we add this value to the height of the tower:
ℎ
=
�
+
150
meters
=
56.016
meters
+
150
meters
=
206.016
meters
h=H+150 meters=56.016 meters+150 meters=206.016 meters
Therefore, the height of the observer's eye level above the ground is approximately
206.016
206.016 meters.
The correct answer is:
F) 125.1 meters
