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November 15th, 2018, 11:17 AM   #1
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Struggling with Angle Problem

Hello, and thanks to anyone who can help me solve this problem.

The question I'm struggling with is as follows:

You have a square base in a plane. Say for example, 3 cm wide base with 3 cm length. Think of it as the bottom of a box.

You want to create sides that rise up in the third dimension (height) but at an angle yet to be determined. Think of it as similar to an open box, but rather than having walls with 90 degree angles from the square base as a normal box would, the angle of the walls flare out, and can be variable.
The base of all four walls will connect to square 3x3 base, so they will all have length 3 cm.

1. What is the formula for how long the top of the walls will be for any given angle, with a wall height of 1 cm?

2. What is formula if the height of the walls are variable?

If the wall created a normal box at 90 degrees, for example, at height = 1 it would simply be a 3 x 1 rectangle. With unknown height (h) is would be 3 x h.

TIA
-Mark
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November 15th, 2018, 01:42 PM   #2
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If each wall would have a height h if vertical, but leans out at an angle of u (90 degrees for vertical), the top edges of the walls form a square whose side length is 2h × cos(u) greater than the side length of the base.
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