Question 1117751
There is a non-right triangle with angles at the bottom, 120 degrees, 30 degrees, and angle at the top of 180-30-120=30 degrees.  This triangle is an isosceles triangle, with x being one of the two congruent sides.


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The first right triangle before the man walks the x distance:
r, distance from man to top of cliff

{{{120/r=sin(60)}}}

{{{r/120=1/sin(60)}}}

{{{r=120/sin(60)}}}

{{{r=120/(sqrt(3)/2)}}}

{{{r=240/sqrt(3)}}}

{{{r=240sqrt(3)/3}}}

{{{r=80*sqrt(3)}}}

{{{r=138.56*meters}}}---------which should also be the value of x, in this example problem.