Quod Erat Demonstrandum


Can you draw…

Filed under: NSS — johnmayhk @ 5:57 上午

以下是某道 core math 的題:

Can you draw a triangle with area of 100 cm^2, and two of its sides are 10 cm and 16 cm long? Explain briefly.


100=\frac{1}{2}(10)(16)\sin \theta



Can you draw a triangle with area of 70 cm^2, and two of its sides are 10 cm and 16 cm long? Explain briefly.


No, I can’t. Because I cannot construct \theta which is exactly a solution to \sin\theta = \frac{7}{8}.


No, I don’t have a protractor.



3 則迴響 »

  1. Draw a right-angled triangle with hyp = 4, base = 1 -> height = rt 15
    Draw a right angled triangle with base = rt 15, height = 7 -> hyp = 8
    Then we can obtain the req. angle.
    Ruler is enough to reach this task.

    迴響 由 — 2011/09/08 @ 1:18 上午 | 回覆

    • 楓, Thank you for your reply.

      How to construct exactly 90^o by using ruler only ?

      In theory, it is easy to construct the required \theta by using compass and straightedge (ruler).


      1.Draw a line, say L.
      2.Mark a point on the line, say A.
      3.Draw an circular arc centred at A, intersecting L at B and C (say) by using compass.
      4.Draw two circular arcs with same radii, centred at B and C respectively, intersecting at D.
      5.Join AD, then AD is perpendicular to L.
      6.Fix a unit length.
      7.Use compass to copy the unit length, start from A, construct 7 units, mark the point E on L such that AE = 7 units.
      8.Use compass to copy the unit length, construct 8 units.
      9.Draw a circular arc centred at E with radius 8 units, intersecting AD at F.
      10.\angle AFE is the required.

      However, I just “say" the procedure (in theory) and do nothing in practice. I really don’t know whether I can draw an angle \theta exactly being an acute angle satisfying \sin\theta =\frac{7}{8} or not, even I’m given tools like paper, ruler, compass, pencil whatever. There may always be errors in human eyes and hands, how can I ensure the construction is error-free? If I’m given a super graphic computer to create the angle, but, the original question is “can you draw…", I can “order" the computer to “draw", however, it is not drawn by me.

      If students give the above as a reply to the original question, is it acceptable? Or, should the question be rephrased?

      迴響 由 johnmayhk — 2011/09/08 @ 5:09 上午 | 回覆

  2. i NOTICE THAT the angle is an irrational number similar to Pi. Even you can use the super computer in japan. the computer can’t draw an accurate angle. ^_^

    迴響 由 Toi — 2011/12/04 @ 8:43 上午 | 回覆

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