## Two Triangles

I have a plastic triangle with a 45-degree angle. I lay a square, flat piece of cardboard on it and now the cardboard is at a 45-degree angle with the table. I have a second plastic triangle with a 30-degree angle. I place this triangle under the cardboard, such that it rests on the table, next to the 45-degree triangle. Now, the top edge of the 30-degree triangle doesn't reach the cardboard, so I rotate it around the 30-degree vertex until the top edge is against the cardboard, the bottom edge is on the table, and the vertex touches the vertex of the 45-degree triangle. (At all times, the triangles are held vertical.)

The end result of this is that both triangles appear to have 45-degree angles when viewed along the edge of the cardboard.

1. What is the angle between the two triangles (i.e. the angle on the table between the sides resting on the table)?
2. If I were to draw a line on the cardboard along the 30-degree triangle, then raise the cardboard, what angle would I measure between the bottom of the cardboard and that line?
Can you generalize this? Given an angle A and an angle B < A, what would be the horizontal angle between them, such that they would both look like angle A when viewed perpendicularly to the plane of A?

Source: Original.

Solution
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