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    == 4.856.5440180B

    cmbb

    B

    b

    A

    a

    39.104.85sin40sin

    7.6

    sinsin

    =

    =

    =

    cmbCB 39.10and6.54,4.85 ===

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    2. In the triangleABC,AB = 5cm, BC =10cm,

    CA = 8cm, If X is the mid-point of themedian

    AA, find the length ofBX.

    =+=

    +=

    ==

    4.52

    cos)10)(5(21058

    cos))((2

    5''

    222

    222

    B

    B

    BBCABBCABAC

    cmCABASolution:

    A B

    C

    10cm

    5cm

    8cmA

    X

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    cmAAXA

    cmAA

    AA

    BBAABBAABAA

    2075.2'

    2

    1'

    415.4'

    4927.19

    4.52cos)5)(5(255'

    cos)')((2''

    222

    222

    ==

    ==

    +=

    +=

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    ( )

    cmBX

    BX

    AXABAXABABX

    A

    49.4

    1268.20

    8.63cos)2075.2)(5(22075.25

    'cos)')('(2''

    8.634.521802

    1'

    222

    222

    ==

    +=

    +=

    ==

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    3.

    D

    BA

    P

    C

    bb

    a

    a

    For rectangleABCD shown

    in the figure above,AB =BC = b.The foot of theperpendicular fromA to BDis P. Calculate the lengthsofAP and CP.

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    Solution

    :

    2222

    22

    2222

    sin

    sin

    ba

    abAPa

    AP

    ba

    b

    a

    AP

    AB

    APABD

    ba

    b

    BD

    ADABD

    baABADBD

    +==+

    ==+

    ==

    +=+=

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    D

    P

    C

    a

    CDPDPCDDPCDCP

    ba

    aCDP

    ABDCDP

    +=

    +=

    =

    cos))((2

    costhen

    222

    22

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    ( )( )

    ( ) ( )

    ( )

    21

    22

    2244

    22

    2244

    22

    224224

    22

    224222

    2222

    22

    22

    22

    222

    2

    2

    2

    cos))((2

    ++

    =

    ++

    =+

    ++=

    + ++=

    +

    +

    ++=

    +=

    ba

    babaCP

    ba

    baba

    ba

    babbaa

    bababbaa

    ba

    a

    ba

    ba

    ba

    ba

    CDPDPCDDPCDCP

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    4. In the triangle PQR, PQ = a, QR = a + d, RP

    =a+2d, and , where a and

    dare

    positive constants. Show that

    > 120PQR.

    3

    2ada 1200

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    ( )

    ( ) ( )

    dada

    dad

    dada

    dada

    adadadaadada

    daadaada

    PQRQRPQQRPQPR

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    ( )

    ( ) ( )( )

    ad

    ad

    adadadaadada

    daadaada

    QRPQQRPQPR