Question

a 10 - foot ladder leans against a wall; the base of the ladder is 2 feet away from the wall. to the nearest tenth of a foot, how far up the wall does the ladder reach? 2 of 11 questio 9.9 ft 10.2 ft 10.1 ft 9.8 ft

Explanation:

Step1: Apply Pythagorean theorem

Let the height up the wall be \(h\). The ladder length \(c = 10\) (hypotenuse), base \(a=2\). By \(a^{2}+h^{2}=c^{2}\), we have \(h^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(c = 10\) and \(a = 2\) into \(h^{2}=c^{2}-a^{2}\), so \(h^{2}=10^{2}-2^{2}=100 - 4=96\).

Step3: Solve for \(h\)

\(h=\sqrt{96}\approx9.8\) (rounded to the nearest tenth).

Answer:

9.8 ft