SOLUTION: A man standing a certain distance from the base of a cliff notices that the angle of elevation is 60 degrees. After walking x metres away from the cliff, the angle of elevation to

Algebra ->  Trigonometry-basics -> SOLUTION: A man standing a certain distance from the base of a cliff notices that the angle of elevation is 60 degrees. After walking x metres away from the cliff, the angle of elevation to       Log On


   

Question 1117751: A man standing a certain distance from the base of a cliff notices that the angle of elevation is 60 degrees. After walking x metres away from the cliff, the angle of elevation to the top of the cliff has decreased 30 degrees. If the cliff is 120m high, find x correct to the nearest cm.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fr=sin%2860%29
r%2F120=1%2Fsin%2860%29
r=120%2Fsin%2860%29
r=120%2F%28sqrt%283%29%2F2%29
r=240%2Fsqrt%283%29
r=240sqrt%283%29%2F3
r=80%2Asqrt%283%29
r=138.56%2Ameters---------which should also be the value of x, in this example problem.