@Mike - that's roughly the best way i've found if you're trying to create a kite knowing the long lengths are, say, 100mm and the included angle is, say, 58 degrees.

draw a horizontal line 100mm.
ctrl+k and then in info bar change rotation point to left center and in info bar rotate the copy 29 degrees (1/2 of total) and stretch the length by grabbing to top right corner handle creating a long center reference line.
again ctrl+k the original line, change rotation point, rotate 58 degrees. you end up with an arrow shape.
then using shape tool and either of the lines, just add some random point from the end and then drag/snap the added point to the center reference line. then repeat again but then drag it to the origin creating a shape. (half of the kite)
delete the reference line.
repeat using the other line but now drag/snap the added end-point to the other new end-point and then again add and drag/snap to the origin.
now add the shapes. now you have a kite with the long sides equaling 100mm and the included angle of 58 degrees.

sounds complicated but it's not