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woodruffk · Sep 7, 2011, 09:03 PM

A building is 3 feet away from a nine foot fence that surrounds the property. A worker needs to wash a window in the buidling that is 14 foot from the ground. He wants to place a ladder over the fence so it leans against the building. He decides to to place the ladder nine foot from the building. To the tenth of a foot, how long of ladder will he need

jcaron2 · Sep 7, 2011, 09:18 PM

The base of the ladder is 9' from the building, while the fence is 3' from it. Hence, the base of the ladder is 6' from the fence. In that 6' distance, the ladder has to go up at least 9' to get over the fence. Hence it has a slope of at least 9/6 = 1.5 (i.e. the ladder goes up 1.5' for every 1' of distance it covers over the ground). In all the ladder covers 9' of ground between its base and the side of the house. At a slope of 1.5, the top of the ladder would therefore be 13.5' above the ground. (Another way to look at this would be that the ladder passes over the top of the fence 9' off the ground with a slope of 1.5' of rise for every 1' of run. Thus in the remaining 3' between the fence and the house, the ladder would go up an additional 4.5' for a total height of 13.5'). I would think a ladder 13.5' in the air would be high enough to wash a 14' window.

Now to find the required length of the ladder you need to use the Pythagorean theorem:

$L^2=9^2+13.5^2$

$L=\sqrt{263.25}$

$L \approx 16.2$ feet.

Does that make sense?

panda2913 · Oct 3, 2011, 04:05 PM

Mkay, so you know that the building is 3 feet away. That's like 1 yard or the length of both of your arms together. The ladder has to be at least 14 feet. Now do this: Put your arm on a table and measure it against a wall. Put a landmark or something there. Then tilt you arm like the ladder in this problem. As you can see, the point of the wall that your arm is now touching is further down from your original spot. Use this to help you answer your question!