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Mt. Tsouris

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Submitted By emilyhahn3
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Mount Tsouris Ski Area I have been asked by Mount Tsouris Ski Area to find the angle of elevation at which the ski lift will take the least time. I plan to find this, by first find the missing measurement on the bottom, given the information,. Then, finding the height of the mountain so that I can find the length of hypotenuse(the length of the cable) and find how long it takes to get up that length. In the process of finding how long it takes the cable car to travel at a certain angle I, at first, had to get the missing length of the bottom, so I made that missing length x then put that tan33°=height/(800+x). And since there is two variables in that equation I chose to solve for the height and got that height=(800+x)(tan33°). But, I still had to get rid of the height, so I found another equation that was true for the height and so I found that tan35°=height/x, which when you solve for height comes to be height=x•tan35°. Then, I set those two height equations equal to each other so that, (800+x)tan33°=x•tan35°. Then I used the equations: tanø=(height of mountain/length of adjacent side) to find the bottom length of each degree(if needed), and sinø=(height of mountain/length of hypotenuse) to find the hypotenuse of each degree(the length of the cable car). To convert the feet to miles, since the speed is in miles/hour, I took the hypotenuse and divided it by 5280 feet(the number of feet in a mile) to get the mile. Then I multiplied that total by the reciprocal of the mph(to find the mph for each degrees, subtract .125 for each degree, or .25 for 2 degrees). Then, I multiplied that total by 60 to get the time from hours to minutes.≤ Then, I compared all the different degrees and how long they take, to see which is the fastest. See Appendix A for greater detail of my work. After doing all calculations, I conclude that although they are all very close, that 34° will take the skiers up the lift the fastest. For 35° I got 29.856 min, for 34.5° I got 29.85 min, for 34 I got 29.844 min, for 33.5° I got 29.856 min, and for 33° I got 29.88 min. Although I found that 34° to be absolutely the quickest, I found that they were all very close and that no matter what, any of them would get the skiers up in about the same amount of time.…...

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