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Math Help - finding the grade of a mountain trail

  1. #1
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    finding the grade of a mountain trail

    a straight trail with a uniform inclination leads from a hotel, elevation 5000 feet, to a lake in a valley, elevation 4100 feet. The lenght of the trail is 4100 feet. what is the inclination ( grade) of the trail

    i'm not a native speaker of english , tha's why i don't really understand...i hope u guys can help me
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  2. #2
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    Hello alessandromangione
    Quote Originally Posted by alessandromangione View Post
    a straight trail with a uniform inclination leads from a hotel, elevation 5000 feet, to a lake in a valley, elevation 4100 feet. The lenght of the trail is 4100 feet. what is the inclination ( grade) of the trail

    i'm not a native speaker of english , tha's why i don't really understand...i hope u guys can help me
    The usual way of giving the grade of a hill is as a percentage. It is calculated from the formula:
    Percentage grade = \frac{\text{vertical distance}}{\text{horizontal distance}}\times 100 %
    If the incline is very small, this is approximately the same as:
    Percentage grade \approx \frac{\text{vertical distance}}{\text{distance along slope}}\times 100 %
    In the question you have been given, the vertical distance = 5000-4100=900, and the distance along the slope = 4100. This is quite a steep incline, so it's not a good idea to use the second formula. So we use Pythagoras' Theorem to work out the horizontal distance:
    Horizontal distance = \sqrt{4100^2-900^2}=4000
    So, using the first formula:
    Percentage grade = \frac{900}{4000}\times 100 % = 22.5 %
    Grandad
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  3. #3
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    My mind is going! I first read the title as "Find the grade of a mountain troll". I believe I had a class with one of those once. As I remember, his grade wasn't very good.
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  4. #4
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    Yes, I've had my share of them as well!

    Grandad
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    thanks grandad
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