Question

to the nearest foot, what is the distance from the base of the building to where the ladder touches the building? 6 ft

Explanation:

Step1: Apply Pythagorean theorem

Let the distance from the base of the building be \(x\). The ladder length is the hypotenuse \(c = 25\) ft (assuming the ladder length is 25 ft as it's a common problem setup, though not shown in the image clearly, but from the options and right - triangle context). The height on the building \(a = 6\) ft. By \(c^{2}=a^{2}+x^{2}\), we get \(x^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 25\) and \(a = 6\) into \(x^{2}=c^{2}-a^{2}\). So \(x^{2}=25^{2}-6^{2}=625 - 36=589\).

Step3: Calculate \(x\)

\(x=\sqrt{589}\approx24.27\approx24\) (rounded to the nearest foot).

Answer:

24 feet (Option D)