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We present a detailed study of the viewing angles of the LMC disk plane. Wefind that our viewing direction differs considerably from the commonly acceptedvalues, which has important implications for the structure of the LMC. Thediscussion is based on an analysis of spatial variations in the apparentmagnitude of features in the near-IR color-magnitude diagrams extracted fromthe DENIS and 2MASS surveys. Sinusoidal brightness variations with apeak-to-peak amplitude of approximately 0.25 mag are detected as function ofposition angle, for both AGB and RGB stars. This is naturally interpreted asthe result of distance variations, due to one side of the LMC plane beingcloser to us than the opposite side. The best fitting geometric model of aninclined plane yields an inclination angle i = 34.7 +/- 6.2 degrees andline-of-nodes position angle Theta = 122.5 +/- 8.3 degrees. There is tentativeevidence that the LMC disk plane may be warped. Traditional methods to estimatethe position angle of the line of nodes have used either the major axisposition angle Theta_maj of the spatial distribution of tracers on the sky, orthe position angle Theta_max of the line of maximum gradient in the velocityfield, given that for a circular disk Theta_maj = Theta_max = Theta. Thepresent study does not rely on the assumption of circular symmetry, and isconsiderably more accurate than previous studies of its kind. We find that theactual position angle of the line of nodes differs considerably from bothTheta_maj and Theta_max, for which measurements have fallen in the range140-190 degrees. This indicates that the intrinsic shape of the LMC disk is notcircular, but elliptical, as discussed further in Paper II. [Abridged]

Magellanic Cloud Structure from Near-Infrared Surveys. I. The Viewing Angles of the Large Magellanic Cloud