These charts may give you a better perspective :
And your statement about the 60deg 2d beam being equal to the depth is also correct. A 20deg angle beam gives a bottom circle of about 1/3 the depth of the water ... so 3 times that angle would give a bottom circle diameter more or less equal to the depth of the water.
... cp
(chart images taken from my thread on the Lowrance Elite 5 DSI, that's in the Electronics Forum)