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Mathematics Forum
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| Author | Message / Information |
| Andrew234 Quote | Reply | | HELLPP posted on: 8/31/2006 4:55:47 AM Hi all , help im confused, all words are directly from book. Fire trucks with extension ladders are used regularly to remove people from burning buildings. However, they are limited in how far they can reach, by both the length of the ladder and, for stability reasons, the distance they can safely park away from the edge of the building. Assume that the ladder is at the back of the truck and its foot is 2m off the ground. 1.) Draw a diagram and label the unknown distances with pronumerals. PRODUCING: The truck is 4m away from the base of the building and the fully extended ladder reaches 16.46m up the side of the building. 2.) Use your diagram to find the length of the ladder to the nearest metre. 3.) It is decided that the trucks must park between 2m and 7.5m from buildings. What is the maximum height that the ladder can reach from each extreme postion? Thanks guys explain as well im confused. |
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Crazy Horse
Quote | Reply | This message was updated on 9/2/2006 10:10:10 PM by Crazy Horse |
HELLPP
replied on: 9/2/2006 10:09:30 PM I think that I got it. I am not going to draw the diagram, but I will use "b" for the height of the building (where the ladder reaches), "f" for the fire truck's distance from the building, and "l" for the height of the ladder. f = 4 meters, b = 16.46 meters, and l is unknown. From a^2 + b^ = c^2, we have (16.46 - 2)^2 + (4)^2 = l. The reason you need to subtract 2 from the bulding is because the base of the ladder is 2 meters up due to the fire truck. This gives us l = 15.00 meters (rounding to the nearest hundreth). So the length of the fully extended ladder is 15.00 meters. If the truck is 2 meters away from the bulding, then we have (2)^2 + (b - 2)^2 = (15)^2. So 4 + b^2 - 4 = 225, or b = 15. Adding 2 meters gives us 17 meters (again, because the fire truck is 2 meters off of the ground). If the truck is 7.5 meters away from the building, then we have (7.5)^2 + (b - 2)^2 = (15)^2. So 56.25 + b^2 - 4 = 225 or b^2 = 172.75. That leaves us with b = 13.14 meters, and adding 2 gives us 15.14 meters. I hope this helps you! |
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Andrew234
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HELLPP
replied on: 9/5/2006 5:21:14 AM Thanks for the hep, but what i dont understand is , if you drew up the diagram, you would find that the length of the truck is unknown... how can you find the length of the hypotenuse if the length of the truck is unknown? and how can you find out how far up the ladder reaches with only one number , the height of the building? |
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