Is there a good way to lay out a right angle?
Step #1: Finding the center.

Never built a round deck before, but to find out where you want to put the deck, and to mark the center point, I would drive a stake or nail, tie a string to it that is as long as the desired diameter (30' here), and then walk in a circle with it, keeping it taut, and putting some long nails into the ground, at the end of the string, every 3' or so.  Then I'd put a string around all of those nails, wrapping it around each nail a few times.  Alternatively, if you are working on concrete, clean it up and use chalk instead of the nails &amp; strings for the outside.

Step #2: Dividing the circle into quadrants.


Take the string that is attached to the center stake to the edge of the circle and drive a nail/stake there.  (On concrete, just make a mark and get someone to hold it there.)  Attach a second string to that nail and walk to the opposite side of the circle.  PS: The reason you're using the center string here is to MAKE SURE that each mark is 30' from the center, otherwise the math will fall apart.
Once at the other side of the circle, I would drive another nail/stake, making sure that the string going across the entire circle was both (1) taut and (2) passing directly over the circle.  For reference in the next step, we will call these two points Outside Point #1 and #2 (OP1 and OP2.)  If you're on concrete, you can pop a chalk line at this point.
Then, I would use some math.  Dividing the circle into quadrants would require 4 points on the outside of the circle that (of which we currently only have 2), if you were to draw lines in between all of them, would form four right triangles (with the right angle in the center, which is what you're asking for.)  Knowing that each leg of each right triangle needs to be 30', the hypotenuse of each triangle must be 42' 5 (1/8)" -long (square root of 30^2 + 30^2).  Armed with a string of that length, I would attach it to both of nails/stakes/marked points from above, OP1 and OP2, and I would walk to both sides of the circle, near where the other two points, which we'll call OP3 &amp; 4, should be.  Make marks where the end of this string crosses over the outside of the circle (to be exact, you should once again have the 30' center string in your hand.)  See diagram below.  For OP3, make this measurement from both OP1 and OP2, and for OP4, make the measurement once again from both OP1 and OP2.  You should have two marks at both the OP3 and OP4 locations, and they should be so close (within 1") that you can just eyeball an average of them.  Drive a nail at those locations, and draw a taut string from OP3 to OP4, making sure it passes over the center.  Once again, if you're on concrete, pop a chalk line.




I'd imagine that this is the most accurate method outside of buying survey equipment.  Good luck!

(Note: Unfortunately, as you swing a string around a nail/stake, it will shorten in length.  If you decide to trace out the entire outside of the circle, your distance from the center will decrease as you go.  Tying a loop in the string, allowing it to rotate around the nail/stake will prevent this.)