Question

question if you place a 24 - foot ladder against the top of a 22 - foot building, how many feet will the bottom of the ladder be from the bottom of the building? round to the nearest tenth of a foot. answer attempt 1 out of 3

Explanation:

Step1: Apply Pythagorean theorem

Let \(a\) be the distance from the bottom of the ladder to the building, \(b = 22\) (height of the building, one - leg of the right - triangle), \(c=24\) (length of the ladder, hypotenuse of the right - triangle). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(b = 22\) and \(c = 24\) into the formula: \(a=\sqrt{24^{2}-22^{2}}=\sqrt{(24 + 22)(24 - 22)}=\sqrt{46\times2}=\sqrt{92}\).

Step3: Calculate and round

\(\sqrt{92}\approx9.6\) (rounded to the nearest tenth).

Answer:

\(9.6\)