angle FDE = 42 -11 = 31 degrees -------------answer.

angle DEF = 180 -(55 -11) = 136 degrees -----answer.

There are many ways to solve for the height of the cliff.

Since the two angles above are already there, we might as well use them in finding the height of the cliff.

I understand from the figure that the height of the cliff is FG.

In triangle DEF:

angle DFE = 180 -31 -136 = 13 degrees

By Law of Sines,

85/sin(13deg) = (DF)/sin(136deg)

DF = [85/sin(13deg)]*sin(136deg)

DF = 262.4836 meters

So, in the big right triangle,

Height of cliff = 262.4836*sin(42deg) = 175.636 m ---------answer.