To find the distance from the observer to the base of the tower, we can use the tangent function from trigonometry, which relates the angle of elevation, the height of the tower, and the distance from the observer.
The formula we will use is:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Where:
- \(\theta\) is the angle of elevation (65°)
- The opposite side is the height of the tower (200 ft)
- The adjacent side is the distance from the observer to the base of the tower (which we want to find).
Rearranging the formula to find the adjacent side gives us:
\[ \text{adjacent} = \frac{\text{opposite}}{\tan(\theta)} \]
Substituting in our values:
\[ \text{adjacent} = \frac{200 \text{ ft}}{\tan(65°)} \]
Now we calculate \(\tan(65°)\):
\[ \tan(65°) \approx 2.1445 \]
Now plug this into the calculation for adjacent:
\[ \text{adjacent} \approx \frac{200 \text{ ft}}{2.1445} \approx 93.26 \text{ ft} \]
Therefore, the distance from the observer to the base of the tower is approximately 93.26 ft.
Thus, the correct answer is:
93.26 ft.