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Math Help - Law of cosines

  1. #1
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    Smile Law of cosines

    okay i dont know why, this may be extremely easy but i'm just not getting the right answer

    Here's the question:
    richmond is 200 kilometers due east of Teratown and Hamilton is 150 kilometers directly north of Teratown. Find the shortest distance in kilometers between Hamilton and Richmond.

    I use law of cosines right? and so what would the equation look like?
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  2. #2
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    Quote Originally Posted by kri999 View Post
    okay i dont know why, this may be extremely easy but i'm just not getting the right answer

    Here's the question:
    richmond is 200 kilometers due east of Teratown and Hamilton is 150 kilometers directly north of Teratown. Find the shortest distance in kilometers between Hamilton and Richmond.

    I use law of cosines right? and so what would the equation look like?
    Pythagoras' Theorem:

    (200)^2 + (150)^2 = (HR)^2.
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  3. #3
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    but i have to use the law of cosines...how do i do that with this problem? or is just not possible?
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  4. #4
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    Quote Originally Posted by kri999 View Post
    but i have to use the law of cosines... Mr F asks: Why?

    how do i do that with this problem? or is just not possible?
    OK:

    <br />
(HR)^2 = (200)^2 + (150)^2 - 2(200)(150) \cos(90^0) = .....<br />

    In case you haven't guessed, Pythagoras' Theorem is a special case of the cosine rule.
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  5. #5
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    Thank you! I got the same equation but somehow I keep getting the answer wrong, but i just tried a differnet method and it worked out..
    yeah i have to use law of cosines because that's what the chapter's on haha

    thanks so much!
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    OK:

    <br />
(HR)^2 = (200)^2 + (150)^2 - 2(200)(150) \cos(90^0) = .....<br />

    In case you haven't guessed, Pythagoras' Theorem is a special case of the cosine rule.
    I actually didn't know that. I just kinda figured he sat around playing with blocks and rulers for a few weeks until a lightbulb turned on.
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