Question

An 8-foot ladder is leaning against a wall so that the top of the ladder is 5 feet above the ground. If a 15-foot ladder is leaned against the wall and forms the same angle with the wall, how high up the wall does this ladder reach? Enter your answer in the box. Show your answer to thousandths.

Answer 1

Let's call the height the 8-foot ladder reaches on the wall "h1", and the height the 15-foot ladder reaches on the wall "h2". We can set up a proportion to find h2, using the heights and lengths of the ladders:

(h2 + 5) / 15 = (h1 + 5) / 8

We can cross multiply to solve for h2:

15 * (h1 + 5) = 8 * (h2 + 5)
120 + 75 = 8h2 + 40
195 = 8h2 + 40
155 = 8h2
h2 = 19.375 feet

So the 15-foot ladder reaches 19.375 feet up the wall