To determine if Camila can reach the window with her 20 ft. ladder, we need to consider the vertical height of the window and the length of the ladder.
Since the bottom of the window is 16 ft. from the ground, she needs to extend the ladder vertically to at least this height. A 20 ft. ladder is sufficient to reach the required height, as it is longer than 16 ft.
However, if Camila needs to lean the ladder against the wall, we should consider the angle at which the ladder will be positioned. Generally, it’s recommended to place the base of the ladder about 1/4 of the ladder’s length from the wall for safety.
Here’s how it works:
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Distance from the wall: If she leans the 20 ft. ladder at a safe angle, the base of the ladder should be about \( \frac{20 \text{ ft}}{4} = 5 \text{ ft} \) from the wall.
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Height the ladder reaches: The height that the ladder reaches can be determined using the Pythagorean theorem. If the base of the ladder is 5 ft from the wall, and the ladder is 20 ft long, we can calculate the height (h) it reaches: \[ h^2 + 5^2 = 20^2 \] \[ h^2 + 25 = 400 \] \[ h^2 = 375 \] \[ h \approx 19.36 \text{ ft} \]
Since the ladder can reach approximately 19.36 ft when placed 5 ft away from the wall, it is more than sufficient to reach the 16 ft height of the window.
Thus, Camila can safely use her 20 ft. ladder to reach the window that is 16 ft above the ground.
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