Let me guess:

There is a triangle ABC where

a = BC = 9.27

b = AC

c = AB

beta = angle B = 27.5 degrees

upsidedown theta (phi?) = angle A = 54.5 degrees

theta = angle C

If my guess is right, then,

theta = 180 -27.5 -54.5 = 98 degrees -----------answer

By Law of Sines,

9.27 /sin(54.5deg) = b /sin(27.5deg)

Multiply both sides by sin(27.5deg),

(9.27*sin(27.5deg) /sin(54.5deg) = b

b = 5.26 -------answer.

By Law pof Sines again,

9.27 /sin(54.5deg) = c /sin(98deg)

Multiply both sides by sin(98deg),

(9.27*sin(98deg) /sin(54.5deg) = c

c = 11.28 -------answer.