Question 91489
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.