求斜坡與水平地面所成之角度大小

Let the other end of the slope be X, that is XQ = 0.8. Length of sun ray (dotted line) = XP.
Let Y be a point on XP such that QY is perpendicular to XP.
Angle XPQ = 90 - 70 = 20 degree.
sin (Angle XPQ) = QY/PQ = QY/1 = sin 20
so QY = 1 x sin 20 = sin 20 ............(1)
sin (Angle YXQ) = QY/QX = QY/0.8
so Angle YXQ = arcsin ( QY/0.8) = arcsin ( sin 20/0.8) = 25.31 degree
so angle between slope and the horizontal ground = 70 - 25.31 = 44.69 degree.

2013-05-22 19:11:02 補充：
For the other method, this belongs to the type of equation : a sin x + b cos x = c, which is only taught in M2 syllabus, not in core maths.

上去睇咪知...
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