Final answer:
The base of the ladder is approximately 20.7 feet from the wall.
Step-by-step explanation:
To find the distance between the base of the ladder and the wall, we can use trigonometry. The base of the ladder forms a right triangle with the ground and the wall. The length of the ladder is the hypotenuse of the triangle, and the angle between the base of the ladder and the ground is given as 50°.
We can use the sine function to find the length of the side opposite the angle (the distance between the base of the ladder and the wall). The formula is sin(angle) = opposite/hypotenuse. Plugging in the values, we have sin(50°) = opposite/27 feet.
Solving for the opposite side, we get opposite = sin(50°) * 27 feet ≈ 20.7 feet. Therefore, the base of the ladder is approximately 20.7 feet from the wall.