Question

a ladder is leaning against a vertical wall. the distance from the top of the ladder to the base of the wall is 24 feet. the distance from the base of the wall to the bottom of the ladder is 4 feet. what is the length of the ladder? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 24\) (height), \(b = 4\) (base), and \(c\) is the length of the ladder.
Substitute values: \(24^{2}+4^{2}=c^{2}\).

Step2: Calculate squares

\(24^{2}=576\), \(4^{2}=16\).
So, \(576 + 16=c^{2}\), which is \(c^{2}=592\).

Step3: Find \(c\)

\(c=\sqrt{592}\approx24.3\).

Answer:

\(24.3\)