Answer:
1190.35 ft
Step-by-step explanation:
The figure for the given scenario is shown below.
From the triangle Δ ABC, AB is the height of mountain, BC is the distance of campsite from the foot of mountain and [tex]\angle A[/tex] is the depression angle.
So, [tex]AB=1700\textrm{ ft},\angle A=35[/tex]°
Let the side BC be [tex]x[/tex] ft.
Now, the tan of the angle A is given as:
[tex]\tan (\angle A) =\frac{BC}{AB}[/tex]
Plug in [tex]x[/tex] for BC, 1700 ft for AB and 35° for [tex]\angle A[/tex]. Solve for [tex]x[/tex]. This gives,
[tex]\tan (35)=\frac{x}{1700}\\x=1700\times \tan (35)=1190.35\textrm{ ft}[/tex]
Therefore, the distance of campsite from the foot of the mountain is 1190.35 ft.
