But I can't help but think that a there may be some obvious way to lay it out.

I know - give the job to a carpenter!

Let me see ... they would mark lines 2' in from the outer border, and form a rectangle. Then they would probably draw a circle around one corner 2' in radius, then put a nail in the other corner, attach a string, and run the string so it was tangent to the circle at the first corner!

So, it would look a bit like your solution, then!

]]>As you can see, the trick is to extend the beam out just enough till it touches the uper left corner and the required lengths and angles can be found as shown. Once you have these, the solution to the problem is easily attainable.

]]>I shall reveal the solution to the problem momentarily.

]]>If they **are **congruent, then we need to find the gap "B" (=12-A)

And the gap "B" will be a function of the angle θ

And θ will be a function of "B"

Round and round we go ...

]]>Take a protractor, measure the angle of the triangle, use this and tan to find A.

Problem solved.

]]>The hint is litterally this: "think outside the box".

]]>Then I give up. I'm not quite sure if it is possible since you don't know any of the angles.

Of course, if your father measured one single angle, he would have saved me 30 minutes of work.

]]>]]>

Draw a line from the point of angle y in triangle B to the hypotenuse of triangle A, such that it hits the hypotenuse at a 90 degree angle. Then, draw a line which connects the very top of triangle A to that of B. Call this new triangle, triangle C.

The bottom most angle of triangle C is 90 degrees. Since the hypotenuses in triangles A and B are parallel (assumed), the top left angle in triangle C is equal to angle y in triangle B. Now add the top right angle of triangle C, the 90 degree angle just to the right of it, and angle y in triangle B. Since all these angles put together form a line, they add up to 180 degrees. But we also know that x + y + 90 = 180. Thus, the top right angle in C is equal to angle x. Therefore, triangle C is similar to triangle B and A (assuming these two are congruent).

However, we know that the side of triangle C is 2'. Since the triangles are similar: 6 / 12 = 2 / x, 6x = 24, x = 4. So the other side of triangle C is 4'. This means the hypotenuse of triangle C is about 4.47'.

The length of the entire bottom is 12 feet, 12 - 4.47 = 7.53'.

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