SUDUT ANTARA DUA GARIS BERSILANGAN by anamaulida

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									                                                                                H
    SUDUT ANTARA DUA GARIS                                                                          G
    BERSILANGAN
                                                                        E                   F               (BG,FH) =  (BG,BD)
                                                                                                                        =  (DBG)
                                                                                                                        = 60 º
                                                                                D                          segitiga DBG sama sisi
                                                                                                    C
                                                                        A                   B

                                                                                H
                                                                                                    G
                                                                                                           (AB,DF) =  DC, DF)
                                                                                                                       =  (CDF)
                                                                        E                   F             sin  (CDF) = CF/DF
     ( m, n)             =            (m, n’)                                                                   a 2 1
                                                                                                                           6
                                       (m’, n)                                 D
                                                                                                    C
                                                                                                                  a 3 3

                                       (m’’, n’’)                      A                   B

    m // m’ // m’’        dan n // n’ // n’’
                                                                            H
                                                                                                G           (AG,FH) = 90º
                                                                                        F
    SUDUT ANTARA GARIS DG BIDANG                                                                           AG ┴ CFH → AG ┴ CF
                                                                                                                 → AG ┴ CH
                 g            A                                             D                                    → AG ┴ FH
                                                                                                C
                                                                    A                   B
                                                                                                           (BH, ABCD) =  (BH,BD)
                                                                            H
                                                                                                G
                                            O      α                                                                  =  (HBD)
           g’        A’                                             E                   F
                                                                                                         tan  (HBD) = DH/DB
                                                                                                             a    1
                                                                                                         =         2
                                                                            D                              a 2 2
                                                                                                C
     ( g , α)            =            (g, g’)                     A                   B
                                       AOA’                                H
                                                                                                G          (CG,BDG) =  (CG,CX)
    sudut antara grs g dg bid α adalah sudut antara                                                             =  (CGX) =  (CGO)
     grs g dengan proyeksinya pada bid α            E                                   F
                                                                                                          cos  CGO = CG/GO
                                                                                                                     a   1
    SUDUT ANTARA DUA BIDANG                                                                                      =         3
                                                                            D                                      a 3 3
                                                                                                C
                                                                    A                   B
                 β                m
                              A
                                                                D                                          DABC bid-4 siku-2, di A
                                                ( α, β)                                                    AB =AC = 6 , AD = 4
                     O                                                              X                       (AD,BCD) =  (AD,DX)
                                                                                                               =  ADX=  ADP
             α                        n                                                                 C tan  ADP = AP/AD
                                  B                                                                      C
                                                                                                                    3 2
                                                                A                               P               =
     ( α, β )            =  ( m, n)                                                       B
                                                                                                                     4
                              AOB                                                  T
    Grs m (OA) pada bid β, dan
                                                                                                        T ABCD limas segi -4 beraturan
        m tegaklurus garis (α, β)
                                                                                                        AB =4 , AD = 6
    Grs n (OB) pada bid α, dan
        n tegaklurus garis (α, β)                                           D                            (AT,ABCD) =  (AT,AO)=  TAO
                                                                                                        Cos  TAO =AO/AT =
                                               CONTOH                                               C                       2 2
                                                                                O
       H                                                    A                                                                6
                          G                                                             B
E                F
                               (AB,FH) =  (AB,BD)                                                      (AT,TBD) =  (AT,TO)=  ATO
                                                =  (ABD)
                                                                                                        tan  ATO =AO/OT =
                                                                                                                            2 2 1
                                                = 45 º                                                                            14
                                                                                                                                 2 7     7
      D                                                                                                 ( TO = √ (36-8)=√28 = 2√7)
                          C
A                B

								
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