F.4 Maths Trigonometry(2)

YTC

2015-06-11 4:02 am

question: http://postimg.org/image/6818gavb5/
solution: http://postimg.org/image/l2ptuh4w1/

For part(c), I think that VE should be the projection of VC on VBD.
But why in the solution, it adds a point H and the required angle becomes angle
HVC.

What is/are the mistake(s) I have made?
Please teach me. Thank you!~

回答 (1)

用戶45314

2015-06-11 9:05 am

✔ 最佳答案

It is because the right pyramid has a rectangular base but not square base.
CE is 丄 to VE but CE is not the shortest distance to plane VBD (or you can say the line BED)
As you see in the solution, CH is the shortest distance which is 丄 to BED.

2015-06-11 17:28:17 補充：
CE is not 丄 BED (as you see in the solution)
We should calculate the shortest distance additionally if the base is not square.

2015-06-11 17:32:53 補充：
Just think about the properties of rectangle and square.
When diagonals are drawn on rectangle and square, the 4 angles at the middle are 90° when it is square but rectangle's are not.
(right pyramid means the apex is directly above the center of the base.)

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