YTC 發問於 科學及數學數學 · 5 年前

F.4 Maths Trigonometry(2)

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!~

更新:

RE Toi Lam:

So actually CE is not 丄 BED?

We should calculate the shortest distance additionally if the base is not square?

1 個解答

評分
  • 5 年前
    最愛解答

    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.)

還有問題嗎?立即提問即可得到解答。