(%i1) Cornelsen S. 97, Nr. 15

(%i2) a) Winkel im Seitendreieck

(%i3) alpha = beta = 55,55°

(%i4) gamma = 68,90°

(%i5) b) Winkel ASC = 106,26°

(%i6) Winkel SBT = 2 * 36,87° = 73,75°

(%i7) c) O = 8 * Seitendreieck = 8 * 11,6666 = 93 1/3 FE
  
(%i8) Cornelsen S. 97, Nr. 16

(%i9) a) B(8|8|0), C(0|8|0), D(0|0|0),

(%i10) E(6|2|5), F(6|6|5), H(2|2|5)

(%i11) b) Winkel ABF = 68,2°

(%i12) d) O = 8 * 8 + 4 * 4 + 4 * Trapez
     = 64 + 16 +  4 * 30 = 200 FE 

(%i14) c) Diagonale BH und DF

(%i15) Zwei Punkte B, H der Gerade g


(%i16) B : transpose(matrix ([8.0,8.0,0.0]));
                                    [ 8.0 ]
                                    [     ]
(%o16)                              [ 8.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i17) H : transpose(matrix ([2.0,2.0,5.0]));
                                    [ 2.0 ]
                                    [     ]
(%o17)                              [ 2.0 ]
                                    [     ]
                                    [ 5.0 ]

(%i18) Aufpunkt stuetzvec


(%i19) stuetzg : transpose(matrix ([8.0,8.0,0.0]));
                                    [ 8.0 ]
                                    [     ]
(%o19)                              [ 8.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i20) Richtungsvektor uvec


(%i21) uvecg : H - B;
                                   [ - 6.0 ]
                                   [       ]
(%o21)                             [ - 6.0 ]
                                   [       ]
                                   [  5.0  ]

(%i22) x-Vektor xvec


(%i23) xvec : transpose(matrix ([x,y,z]));
                                     [ x ]
                                     [   ]
(%o23)                               [ y ]
                                     [   ]
                                     [ z ]

(%i24) Zwei Punkte D, F der Gerade h


(%i25) D : transpose(matrix ([0.0,0.0,0.0]));
                                    [ 0.0 ]
                                    [     ]
(%o25)                              [ 0.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i26) H : transpose(matrix ([6.0,6.0,5.0]));
                                    [ 6.0 ]
                                    [     ]
(%o26)                              [ 6.0 ]
                                    [     ]
                                    [ 5.0 ]

(%i27) Aufpunkt stuetzvec


(%i28) stuetzh : transpose(matrix ([0.0,0.0,0.0]));
                                    [ 0.0 ]
                                    [     ]
(%o28)                              [ 0.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i29) Richtungsvektor uvec


(%i30) uvech : H - D;
                                    [ 6.0 ]
                                    [     ]
(%o30)                              [ 6.0 ]
                                    [     ]
                                    [ 5.0 ]

(%i31) x-Vektor xvec


(%i32) xvec : transpose(matrix ([x,y,z]));
                                     [ x ]
                                     [   ]
(%o32)                               [ y ]
                                     [   ]
                                     [ z ]

(%i33) Schnittpunkt der Geraden g und h


(%i34) sp : transpose(matrix([  4.000000000000,  4.000000000000,  3.333333333333]));
                              [      4.0       ]
                              [                ]
(%o34)                        [      4.0       ]
                              [                ]
                              [ 3.333333333333 ]

(%i35) Schnittwinkel alpha =  61.02°