##
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.

- What is the angle between the two triangles (i.e. the angle on the
table between the sides resting on the table)?
- 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

Mail to Ken