The Solution:
Representing the given problem in the diagram below:
We shall solve for x by applying the Pythagorean Theorem as below:
[tex]\begin{gathered} \text{hyp}^2=opp^2+adj^2 \\ x^2=30^2+10^2 \end{gathered}[/tex][tex]\begin{gathered} x^2=900+100 \\ \\ x^2=1000 \end{gathered}[/tex]
Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{x^2}=\text{ }\sqrt[]{1000} \\ \\ x=31.623\approx32\text{ feet} \end{gathered}[/tex]
Therefore, the length of the ladder to the nearest foot is 32 feet.
Thus, the correct answer is 32 feet.
