There is a point M inside a square ABCD such that angle MAB is 60° and angle MCD is 15°. Find angle MBC.
(In reply to
Solution - another method by Telly)
The three equations you "solve" (x + z = 120, y - z = 15, y + x = 135) are not independent. You derived one from the other two. There are many solutions.
Of the requirements that you list, only that z<90 is apparent from the diagram. But in fact all your requirements are met by quite a range of solutions.
x y z
119 16 1
110 25 10
100 35 20
90 45 30
88 47 32
86 49 34
84 51 36
82 53 38
80 55 40
78 57 42
76 59 44
74 61 46
72 63 48
70 65 50
68 67 52
66 69 54
64 71 56
62 73 58
60 75 60
58 77 62
56 79 64
54 81 66
52 83 68
50 85 70
48 87 72
46 89 74
40 95 80
Where the values for z=30 through z=75 (exclusive of the endpoints) satisfy all your criteria, allowing MBC to be anywhere from 25 to 60 as possibilities.
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Posted by Charlie
on 2004-06-11 13:10:59 |
re: Solution - another method
