A thin rod of length L passes from one vertex of a cube to the opposite vertex. Considering a viewing point in the XY plane only, the rod subtends an angle A with one side of the cube. Considering a viewing point in the XZ plane only, the rod subtends an angle B with the same side of the cube What is the formula for the length of the common side of the cube (X)? The formula for the other two sides will then be: 1. Length X multiplied by the tan of the angle A. 2. Length X multiplied by the tan of the angle B.
2026-04-24 17:58:15.1777053495
Dimensions of a cube given diagonal length and the angles on two perpendicular faces of the cube
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Apply Pythagoras' theorem: $$ X^2+X^2(\tan A)^2+X^2(\tan B)^2=L^2 $$ and solve for $X$.