1. ## Now is this possible?

It's been a while since I was in HS Geometry and I was just wondering if there is a solution to this problem.

Given the lengths of the sides of the dashed line box and the angle between the two lines. Is it possible to find the lengths of the sides of the red box?

 Also the lengths of the two lines is known

2. Originally Posted by joe4325
It's been a while since I was in HS Geometry and I was just wondering if there is a solution to this problem.

Given the lengths of the sides of the dashed line box and the angle between the two lines. Is it possible to find the lengths of the sides of the red box?
Not unless you know the length of line at the lower end of the angle.

Here is an example.

In the attached graph, you know the sides of the black box, and the angle between the two lines, but if the lower line is short, you can see the blue box is small. And if the lower line is long, you can see the red box is large. So these two different boxes (red and blue) can be drawn out of the same starting information. To determine which is correct, you would need more information.

3. oh I forgot, that the lengths of both lines is also known!

Sorry, now how would it be done? :P

[I've edited my original post to reflect this]

4. Originally Posted by joe4325
how would it be done?
Using the attached image as a reference, you know A, B, C, and D.

then

$F = D * sin\left(arctan\left(\frac AB\right) - C\right)$

$F = D * cos\left(arctan\left(\frac AB\right) - C\right)$

note: make sure you do all angles and trig functions in either degrees or radians, but don't mix them.