In the figure, the line of greatest slope of a hillside ABEF makes an angle of 20 degree with the horizontal plane ABCD. C and D are vertically below E and F respectively such that FD = EC = 36 m. BG is a path on the hill such that it makes an angle of 35 degree with the line of greatest slope BE.
a) Find BG.
b) Find the angle between the path BG and the horizontal plane ABCD.
Figure: http://img693.imageshack.us/img693/6936/maths23.jpg
F4 Maths 3-D problems
2010-03-20 9:01 pm
回答 (1)
2010-03-20 9:29 pm
✔ 最佳答案
圖片參考：http://img693.imageshack.us/img693/6936/maths23.jpg
a)EB / BG = cos35°....*
36 / FA = sin20° , FA = 36 / sin20° = EB , sub it to * :
(36/sin20°) / BG = cos35°
BG = 36 / [(sin20°)(cos35°)] = 128.495 m
b)Let the required angle be x :
36 / BG = sin x
36 / {36 / [(sin20°)(cos35°)]} = sin x
sin20° cos35° = sin x
x = 16.27°
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