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Finding an angle

A user submitted this to my site, and it's been unsolved for a couple of days, though he claims it to be fairly simple.

Anyone want to take a look at it? It looks like it doesn't require anything more than the basic geometry...

Wednesday, June 19, 2002

I doesn't look too difficult. My guess is 20 degrees.

If you consider the horizontal distance covered by the three line segments AD,DE and EC, then obviously AD and EC will cover the same horizontal distance but in opposite directions, since the segments are the same length at the same angle. This means that the horizontal distance covered by DE is half the width of the base of the triangle. If the angle we need to find is x, then elementary geometry tells us that the angle between DE and the horizontal plane is 90 -(3*x/2). If DE has length l, then the base of the triangle also has length l. DE covers half this base, and we have the standard formuler
cos (90 - 3x/2) = (l/2) / l
cos (90 -3x/2) = 1/2

seeing as cos (60 degrees) is 1/2 this gives us

90 - 3x/2 = 60
3x/2 = 30
x = 2/3  * 30
x = 20

It's a bit difficult to explain without being able to post a diagram, but I can probably send you one if you don't believe me. :-)


Paul Viney
Wednesday, June 19, 2002

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