Final answer:
To find the distance from the ladder's base to the wall, we apply the cosine function, given the ladder's length and the angle of elevation.
Step-by-step explanation:
To find the distance from the ladder's base to the wall, we can use trigonometry. Given that the ladder forms a right triangle with the wall and the ground, with the ladder as the hypotenuse, the angle of elevation is the angle the ladder makes with the ground. We can use the cosine of the angle of elevation to find the distance from the ladder's base to the wall.
The cosine of an angle in a right triangle is equal to the adjacent side (the side we are looking for) divided by the hypotenuse (the length of the ladder). The formula is:
cos(angle) = adjacent/hypotenuse
Plugging in the values we have:
cos(68 degrees) = distance from wall (adjacent) / 12 feet (hypotenuse)
To solve for the distance from the wall, we multiply both sides of the equation by the hypotenuse:
distance from wall = 12 feet * cos(68 degrees)
Using a calculator, we find:
distance from wall = 12 feet * 0.3746 (cosine of 68 degrees)
distance from wall ≈ 4.4952 feet
Therefore, the distance from the ladder's base to the wall is approximately 4.5 feet.