Question 1200405
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Answer: <font color=red size=4>106.5 feet</font>
This result is approximate.



Explanation:


x = length of wire needed
This is some positive real number.


The image attachment you posted/sent isn't showing up. 
Fortunately the verbal description appears to be sufficient.


From the written description you provided, I'm assuming the diagram looks like this:
{{{
drawing(400,400,-5+2,5+2,-5,5,
line(4,-3,-1,-3),
line(-1,-3,6,3),
line(6,3,4.84,2),
line(4.84,2,2,4),
line(2,4,2.02,-0.41),

locate(1.3,2,"119"),
locate(3.58,0.86,"97"),
locate(-0.29,-2.19,32^o),
locate(3.46, 3.38,"x"),
locate(-3,-4.5,matrix(1,4,"Diagram","not","to","scale"))
)
}}}
Please let me know if my assumption is incorrect.


For the sake of simplicity, we have the following assumptions:<ul><li>The tower is completely vertical.</li><li>The hill is a straight line.</li><li>The slope or gradient does not change anywhere along the hill.</li></ul>Let's draw a red line from the base of the tower and move toward the right a bit.
{{{
drawing(400,400,-5+2,5+2,-5,5,
line(4,-3,-1,-3),
line(-1,-3,6,3),
line(6,3,4.84,2),
line(4.84,2,2,4),
line(2,4,2.02,-0.41),

red(line(2.02,-0.41,2.02+3,-0.41)),

locate(1.3,2,"119"),
locate(3.58,0.86,"97"),
locate(-0.29,-2.19,32^o),
locate(3.46, 3.38,"x"),
locate(-3,-4.5,matrix(1,4,"Diagram","not","to","scale"))
)
}}}


We can slide the 32 degree angle label up and to the right. 
This is because translation/shifting operations preserve the angle measure.
For more information, search out "corresponding angles theorem".


This is what we have when we add that 32 degree label.
{{{
drawing(400,400,-5+2,5+2,-5,5,
line(4,-3,-1,-3),
line(-1,-3,6,3),
line(6,3,4.84,2),
line(4.84,2,2,4),
line(2,4,2.02,-0.41),

red(line(2.02,-0.41,2.02+3,-0.41)),

locate(1.3,2,"119"),
locate(3.58,0.86,"97"),
locate(-0.29,-2.19,32^o),
locate(2.8,0.06+0.3,32^o),
locate(3.46, 3.38,"x"),
locate(-3,-4.5,matrix(1,4,"Diagram","not","to","scale"))
)
}}}
The angle adjacent to this new 32 degree angle is 90-32 = 58 degrees. The two angles 32 and 58 are complementary. They form a 90 degree corner.


Let's add that angle label.
{{{
drawing(400,400,-5+2,5+2,-5,5,
line(4,-3,-1,-3),
line(-1,-3,6,3),
line(6,3,4.84,2),
line(4.84,2,2,4),
line(2,4,2.02,-0.41),

red(line(2.02,-0.41,2.02+3,-0.41)),

locate(1.3,2,"119"),
locate(3.58,0.86,"97"),
locate(-0.29,-2.19,32^o),
locate(2.8,0.06+0.3,32^o),
locate(2.8-0.7,0.06+0.3+0.3,58^o),
locate(3.46, 3.38,"x"),
locate(-3,-4.5,matrix(1,4,"Diagram","not","to","scale"))
)
}}}


There's a bit of clutter, so let's focus on the triangle.
Erase the lines we won't need from this point onward.
{{{
drawing(400,400,-5+2,5+2,-5,5,
line(2.02,-0.41,4.84,2),
line(4.84,2,2,4),
line(2,4,2.02,-0.41),

locate(1.3,2,"119"),
locate(3.58,0.86,"97"),
locate(2.8-0.7,0.06+0.3+0.3,58^o),
locate(3.46, 3.38,"x"),
locate(-3,-4.5,matrix(1,4,"Diagram","not","to","scale"))
)
}}}
At this point, we'll need the Law of Cosines to determine x.


c^2 = a^2 + b^2 - 2*a*b*cos(C)
x^2 = 119^2 + 97^2 - 2*119*97*cos(58)
x^2 = 11336.2838659122
x = sqrt(11336.2838659122)
x = 106.471986296453
x = <font color=red>106.5 feet</font> of wire is needed (approximate).
Make sure your calculator is in degree mode.
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