Hi, I need help with one question, I'm completely confused, so please show me how to work it out. Thanks in advance.


Question:
From point D, the angle of elevation of a cliff top (F) is 42 degrees. After walking 85m along a street inclined at 11 degrees (D to E), the angle of elevation from point E is 55 degrees.
Work out angles FDE and DEF.
Find the height of the cliff.

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.

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Thanks for the help, I get it now.