When a stepladder is placed as shown, is it possible for the lower ends of the ladder to be 12 feet apart? Explain

No, with the guides in between the two ladders, it is not possible for the lower ends of the ladder to be up to 12 feet apart

Step-by-step explanation:

The given parameters are;

The length of two sides of the step ladder = 12 feet

The maximum value allowable for the included angle between the two 12 feet ladders = 58°

Therefore, the maximum value of the third side facing the included angle is given as follows;

let "a" represent the maximum value of the third side formed by the distance apart of the lower end of the ladder, by cosine rule, we have;

a² = 12² + 12² - 2 × 12 × 12 × cos(58°) = 135.383251901

∴ a = √(12² + 12² - 2 × 12 × 12 × cos(58°)) ≈ 11.64

The maximum value of the third side formed by the distance apart of the lower end of the ladder = a ≈ 11.64 feet < 12 feet

Therefore, it is not possible for the lower ends of the ladder to be up to 12 feet apart.

3 is greater then both of those numbers