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Compute the angle between a line and a plane if the line forms the angles of 45 degrees and 60 degrees with two perpendicular lines lying in the plane.

I have no idea how to solve this exercise. I thought that since the line is crossing two lines which are lying in the plane, then the line has two point lying in the plane, and then the whole line lies in the plane and the angle between it and the plane is 0 degrees.

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  • $\begingroup$ Have a look at this en.m.wikipedia.org/wiki/Direction_cosine $\endgroup$ – David Quinn Jan 14 '16 at 20:58
  • $\begingroup$ This exercise is given in textbook for high school students, we haven't learn any analytic geometry. I guess there must be simple way. $\endgroup$ – Planet_Earth Jan 14 '16 at 21:23
  • $\begingroup$ Think of a right angled pyramid which you know the angels that two sides form with the base. Than you need to compute the angel of the line that is the intersection of these two sides. $\endgroup$ – Moti Jan 14 '16 at 21:33
  • $\begingroup$ Any hint how the line intersects the sides? $\endgroup$ – Planet_Earth Jan 14 '16 at 21:40
  • $\begingroup$ Also I can understand how a line will have two points with a plane and wouldn't lie in this plane. This is opposition to the Postulate 5 by Euclid If two points lie in a plane, then the line joining them lies in that plane. $\endgroup$ – Planet_Earth Jan 14 '16 at 21:55
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