To clarify the situation, Camila has a window that is 6 feet high from the ground, and she has a 200-foot ladder that she will place against the wall in such a way that the top of the ladder reaches the bottom of the window.
Given that the window's bottom is at 6 feet, the ladder will form a right triangle with the ground and the wall of the house.
- Height to the windowsill (h) = 6 feet.
Let:
- The length of the ladder (l) = 200 feet.
- The distance from the bottom of the ladder to the wall (d).
Using the Pythagorean theorem:
\[ l^2 = h^2 + d^2 \]
Substituting the known values:
\[ 200^2 = 6^2 + d^2 \] \[ 40000 = 36 + d^2 \] \[ d^2 = 40000 - 36 \] \[ d^2 = 39964 \] \[ d = \sqrt{39964} \approx 199.91 \text{ feet} \]
Therefore, the distance from the base of the ladder to the wall would be approximately 199.91 feet.
This setup indicates that although the ladder is very long, it will be positioned at an angle that allows it to reach the bottom of the window securely and effectively.
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