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Math Help - Help with ladder triangle problem

  1. #1
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    Help with ladder triangle problem

    A 12-foot ladder is leaning across a fence and is touching a higher wall located 3 feet behind the fence. The ladder makes an angle of 60 degrees with the ground. Find the distance from the base of the ladder to the bottom of the fence.

    I am having difficulties with this problem. I think it is 9. Because the entire ladder subtracted from 3 = 9 feet.

    Are my calculations right?
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  2. #2
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    Quote Originally Posted by KevinVM20 View Post
    A 12-foot ladder is leaning across a fence and is touching a higher wall located 3 feet behind the fence. The ladder makes an angle of 60 degrees with the ground. Find the distance from the base of the ladder to the bottom of the fence.

    I am having difficulties with this problem. I think it is 9. Because the entire ladder subtracted from 3 = 9 feet.

    Are my calculations right?
    If the ladder were flat (on the ground) you would be correct,
    HOWEVER,
    "The ladder makes an angle of 60 degrees with the ground."

    Make a sketch (it does not have to be to scale, nor on paper, just create a mental image) of what you have & data given.

    The ladder, wall, & ground represent the three sides of a triangle.
    You know the length of the hypotenuse, that is the length of the ladder or 12 feet.

    The length of the base is:
     = 12 \times \cos (30deg)

    There are a few sin/cos values you should memorize.
    sin(30) & cos(60) is one of them.

    Subtract the distance the fence is from the building, from the base of the triangle, the distance the foot of the ladder is from the building.
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  3. #3
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    12 x Cos(30 degrees)

    Cos 30 = 0.86602540378444 x 12 Length of ladder = 10.395048

    that does not solve this problem..
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  4. #4
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    Quote Originally Posted by aidan View Post
    ...

    The length of the base is:
     = 12 \times \cos (\bold{\color{red}60^\circ})
    ...

    Quote Originally Posted by KevinVM20 View Post
    12 x Cos(30 degrees)

    Cos 30 = 0.86602540378444 x 12 Length of ladder = 10.395048

    that does not solve this problem..
    1. Did you make a sketch as aidan suggested?

    2. If so you must have noticed that aidan made a tiny mistake (see correction)

    3. According to aidan's suggestion you've learned that \cos(60^\circ)=\dfrac12

    4. Now you now that

    x = 12 \cdot \cos(60^\circ) = 6

    5. Therefore the foot of the ladder has a distance of 3' to the bottom of the fence.
    Attached Thumbnails Attached Thumbnails Help with ladder triangle problem-leiteranwand.png  
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