SOLUTION: suppose that 2 poles are 96 feet apart. One pole is 12 feet high, the second one is 52 feet high. There is a wire from the top of each pole to the base on the other pole. How hi

Question 116263: suppose that 2 poles are 96 feet apart. One pole is 12 feet high, the second one is 52 feet high. There is a wire from the top of each pole to the base on the other pole. How high above the ground do the wires cross?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
You MUST draw a diagram and LABEL it to understand what is going on here.
There are 2 right angle triangles formed.
Let the smaller be s and the bigger b.
the smallest angle in s is found by:
tan=opp/adj=12/96=.125
tan^-1(.125)=7.125 deg
The smallest angle for b is also found by
tan=52/96=.541667
tan^-1(.541667)=28.443 deg
We now know 2 angles and an included side of the triangle at the bottom of your diagram that we haven't mentioned as yet.
The 3rd angle in the triangle at the bottom is found by:
180-28.443-7.125=144.432 deg
If we can determine the area of this triangle we can find its altitude which is the answer to this problem. We need to know one more side in order to find the area.
a/sinA=b/sinB
96/sin(144.432)=x/sin(28.443)
x=96*sin(28.443)/sin(144.432)
x=78.6
A=.5ab*sinC
= .5*78.6*96*sin(7.125)
=468 ft^2
Now we can find the altitude of the triangle and our answer.
A=.5ab
468=.5a*96
48a=468
a=9.75 ft Answer
.
Ed
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