三角的應用

2009-08-05 12:41 am
When we observe a distant object,the angle of elevation(or depression)is smaller than that when we observe a nearer object.Explain why.

回答 (1)

2009-08-05 1:29 am
✔ 最佳答案
Let height of distance object = height of nearer object = h for angle comparison purpose.
Let distance of far object from the observer = a
Let distance of nearer object from the observer = b. So a > b.
Angle of elevation of far object = arctan ( h/a)
Angle of elevation of nearer object = arctan (h/b)
Since a > b
so h/a < h/b
so arctan ( h/a) < arctan (h/b)
so angle of elevation of far object < angle of elevation of nearer object.
Same for angle of depression.



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