Final answer:
To find the horizontal distance, use the sine function to find the ratio between the opposite side and the hypotenuse in the right triangle formed by the ladder, the ground, and the wall.
Step-by-step explanation:
To find the horizontal distance between the base of the ladder and the wall, we can use trigonometry. The ladder forms a right triangle with the ground and the wall. The angle of 66° is the angle opposite the base of the ladder.
We can use the sine function to find the ratio between the opposite side (the height of the wall) and the hypotenuse (the length of the ladder). So, we have sin(66°) = opposite/hypotenuse.
Given that the length of the ladder is 16 feet, we can find the horizontal distance by multiplying the hypotenuse by the sine of the angle: horizontal distance = 16 feet * sin(66°).
Rounding the answer to the nearest tenth of a foot, the horizontal distance between the base of the ladder and the wall is approximately 14.2 feet.