Question

a 10 - foot ladder is leaning against the wall. the bottom of the ladder is 4 feet from the base of the wall. which of the following is closest to the distance from the top of the ladder to the base of the wall?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 10\) ft), \(a\) is the distance from the bottom of the ladder to the base of the wall (\(a=4\) ft), and \(b\) is the distance from the top of the ladder to the base of the wall.
So, \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 10\) and \(a = 4\) into the formula:
\(b=\sqrt{10^{2}-4^{2}}=\sqrt{100 - 16}=\sqrt{84}\).

Step3: Calculate \(\sqrt{84}\)

\(\sqrt{84}\approx9.17\) ft.

Answer:

9 ft