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Math Help - Questions about something with a circle

  1. #1
    Junior Member Fnus's Avatar
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    Questions about something with a circle

    Yeah, the title isnt very describing because I wasn't sure what to call it

    The diagram is the one shown below:



    Question 1:
    Using the cosine rule, show that the lenght of AB is

    I don't even know what the question means.
    So any help with that would be appreciated.

    And then there's question no. 2:
    Find the lenght of BP

    Thanks in advance
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, Fnus!


    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .___________
    1) Using the cosine rule, show that: .AB .= .12√2(1 - cos75░)
    If you don't know the Law of Cosines, forget it!


    It says: .AB▓ .= .12▓ + 12▓ - 2(12)(12)cos75░

    . . . . . . .AB▓ .= .288 - 288Ěcos75░ .= .288(1 - cos75░)
    . . . . . . . . . . . - . . . .___________
    Therefore: .AB .= .12√2(1 - cos75░)



    2) Find the length of BP.
    Triangle OBP is a right triangle.
    Angle POB = 37.5░.
    . . . . . . . . . . . . . . . . . BP
    We have: .tan37.5░ .= .---- . . BP .= .12Ětan37.5░
    . . . . . . . . . . . . . . . . . 12
    Therefore: .BP . .9.2

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