SOLUTION: A cable to the top of a tower makes an angle of 35 deg with the lower ground. At a point 100 yards closer to he tower the angle of elevation to the top of the tower is 59 deg. Esti

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Question 91489: A cable to the top of a tower makes an angle of 35 deg with the lower ground. At a point 100 yards closer to he tower the angle of elevation to the top of the tower is 59 deg. Estimate the length of the cable.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the picture; this is important.
Let the height of the tower be "h".
Let the unknows segment of the base be "x"
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h = tan(35)(100+x)
h = xtan(59)
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xtan(59) = 100tan35 + xtan(35)
x = 100tan(35)/(tan59 -tan35)
x = 100tan35/1.619...
x = 43.246...
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Then h = 43.246...*tan59 = 71.9735
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Then using Pytagoras.
catble^2 = h^2 + base^2
cable^2 = 71.9735...^2 + (143.246...)^2
cable = sqrt(25699.60304
cable = 160.31 ft
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Cheers,
Stan H.