Direction requested for this trigonometric window-glass sizing problem

[Fran Jones]

Given this window glass problem:
http://www4.picturepush.com/photo/a/13133012/img/13133012.jpg

Where I have a window opening of the inside dimensions but I
need to order the glass by the outside dimensions, which must
be at least a half inch greater all around, what is the
correct *approach* to the solution of the problem?

That is, given the inside four measurements, how would I
approach the calculation of the outside four measurements?

I think it's going to use my high-school trig, but, I'm not
sure the general approach.

Any mathematical reasoning advice is welcome as I took trig
maybe 40 years ago and haven't used it since. But I do remember
SohCahToa, if that is what I need.

[Fran Jones]

On Wed, 22 May 2013 21:31:42 +0000, Fran Jones wrote:

> Given this window glass problem:
> http://www4.picturepush.com/photo/a/13133012/img/13133012.jpg
>
> Where I have a window opening of the inside dimensions but I
> need to order the glass by the outside dimensions, which must
> be at least a half inch greater all around, what is the
> correct *approach* to the solution of the problem?

Ah, I figured it out. Using symmetry, I put a tiny triangle at the top
of both the right side and the left side, and I figured
out the vertical side!

Due to symetry of parallel lines ...
90° - 34° = 56°
56° divided in half = 28°
90° - 28° = 62°

Given the 62° & 28° angles ...

For the right hand side, I have to add three things:
1/2 inch + the original length + 1/2 tan 62°

So, the length of the right hand side is:
1/2 inch + 48 5/16" + 0.94" = 49 3/4"

Similarly, for the left hand side, I add three things:
1/2 inch + the original length + 1/2 tan 28°

So, the length of the left hand side is:
1/2 inch + 28 7/32" + 0.26" = 29"

For my spreadsheet, given angle "a°" & overlap of 1/2", the
general formula I came up with is the following:

Right side addition = tangent of (90° + a°)/2 * 1/2 inch overlap
Left side addition = tangent of (90° - a°)/2 * 1/2 inch overlap

[Fran Jones]

On Thu, 23 May 2013 02:41:15 +0000, Fran Jones wrote:

> For my spreadsheet, given an angle in degrees & an overlap of 1/2",

> the general formula I came up with is the following:
>
> Right side addition = tangent of (90° + a°)/2 * 1/2 inch overlap
> Left side addition = tangent of (90° - a°)/2 * 1/2 inch overlap

Drat. I just belatedly realized Microsoft Excel has no concept of degrees!

Given the glass opening will be the original length of each vertical side
plus the half inch at the bottom, plus the unknown amount at top...

The unknown right side addition at top = tangent of (90° + angle°)/2 * 1/2 inch overlap
The unknown left side addition at top = tangent of (90° - angle°)/2 * 1/2 inch overlap

Unfortunately, Microsoft Excel does understand degrees, it only knows radians:
RADIANS(angle°)

So, in Microsoft Excel, I will use this as the final formula:
Right side addition at top = tangent of (90° + RADIANS(angle°))/2 * 1/2 inch overlap
Left side addition at top = tangent of (90° - RADIANS(angle°))/2 * 1/2 inch overlap