Ok, lets say this is a 2 dimensional representation of your cone; note this is not to scale.

The sizes you have given are as follows:

120’ Long

26’ wide at it’s base.

Using the calculations for a right angle, cause they are easier, we can determine the following:

r = 13’ (half the base)

h= 120’

We can calculate the Angles:

Tan a = r/h

Tan a = 13/120

a = arcTan 13/120 we get 6.18

This is for one side of the right triangle so if we double the result we get the angle of the Apex (Angle a)

a = 12.36

Now the first rule of a triangle in trigonometry is that the sum of all the angles

** must ** equal 180°

The angles of a base of a cone triangle will be the same, so as we know the angle of the Apex (Angle a) we can determine the two base angles easily.

180° - 12.36 = 167.64/2 = 83.82

So Angles b & c will be 83.82 each. So we now know the following cone angles:

Angle a = 12.36

Angle b = 83.82

Angle c = 83.82

Now with this info we can determine just how wide the cone would be as it grows from the caster, at the Apex. You mentioned that Sirene was standing 18’ from the doorway when she cast her spell. This means that using the angles that we have, which the cone would keep no matter how long it was until it reached it’s maximum length (120’)

So, we can calculate the size of the base of the cone at 18’ (called X) as such:

Tan 12.36 = X/18

X = Tan 12.36*18

X = 3.94’

So basically, the base of the cone would only be

** 3.94’** when it reached the doorway which is 18’ away from Sirene.

Sorry, to bore you all, I know your eyes have glazed over by now.

It is the Engineer in me.

So, now we can say, the Magic overcomes the Trigonometry and the result is exactly as Tann described. I mean after all, the DM is always right, right?