Question

a ladder is leaning against a wall. the base is 8 feet from the wall, and it reaches a height of 11 feet. how long is the ladder? show your work. put your answer in decimal form and round to the nearest tenth. enter your response here

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 8\) (distance from the wall), \(b=11\) (height on the wall), and \(c\) is the length of the ladder.
So, \(c^{2}=8^{2}+11^{2}\).

Step2: Calculate \(8^{2}+11^{2}\)

\(8^{2}=64\), \(11^{2}=121\). Then \(c^{2}=64 + 121=185\).

Step3: Find \(c\)

\(c=\sqrt{185}\approx13.6\) (rounded to the nearest tenth).

Answer:

The length of the ladder is approximately \(13.6\) feet.