What will be the angle of the sun shining on my house throughout the growing season?

Factual Questions
1

Here’s my problem, just in case I’m asking the wrong question: I’m doing a vegetable garden in raised beds. They need sunlight. They’re going in the side yard, to the north of my house (which faces east). The house casts some shade on that yard. That shade ought to get smaller as the angle of the sun changes, right? I need to know where to put these beds (which I just built - two 6x4 beds which will go together to be 12x4) so they’re as close to the house as possible but yet in full sun when they need to be. (They need to be close to the house in case the Historic Commission ever gets around to approving me building a garage - I don’t want to have to move these things once they get full of dirt. I’m bringing in dirt on Tuesday, so this is something of a pressing issue.)

I am thinking this - I know where the shade falls now. If I knew the change in the angle of the sun, I could just, um, remember how to do trig and subtract that angle from the current angle and get the length of the shadow from that, right?

Let’s say April 1 is the date I want full sun on these beds. I live in Columbia, SC. Is there a chart or something for this? How do you go about figuring it?

2

There’s this handy little device, which tells me that today, the maximum angle at which the sun will shine on your plot is roughly 34° – maximum angle to the sun. On April 1st, the sun, having just ten days earlier “passed” the equator, will be at most at 60° degrees. Your maximum solar elevation is, by the way, 80°, on June 21st.

3

Okay, so I’m going to pretend that it’s my cold making me dumb and not the fact that I forgot all the trig I ever knew. (Sorry, Mrs. Murphy.) If the height of the eaves is a, and the current shadow length from the point below the eaves is b, how do I find what b prime will be in April? (Okay, I also forgot how to do superscript. Shoot me.) I know sin is involved (my memory yields “soa-cah-toh”), but I can’t remember how on earth you set this thing up and work it.

All those years of stupid flagpole problems and now that I actually have a real honest to goodness problem to solve with trig I’ve forgotten every bit of it. I do hope this thread hasn’t been dead too long for somebody to take gentle pity on me!