See the diagram below.
In the diagram, alpha represents the angle the pole makes with the ground, while point P marks the edge of the shadow on the ground.
From inspection, we can see that the angles alpha, beta, and 55^o must all sum to 180^o. Furthermore, since the pole makes an angle of 7^o to the vertical, we know that alpha + 7^o = 90^o, and thus alpha = 83^o.
This means that we can calculate beta:
alpha + beta + 55^o = 180^o
83^o + beta + 55^o = 180^o
beta = 42^o
Since we now have /_P, beta, and b, and we are looking for p, the Law of Sines can be helpful here:
sin P/p = sin beta/b
sin 55^o/p = sin 42^o/42
(42*sin 55^o)/(sin 42^o) = p
p ~~ 51.4 "ft"