Answer:
<em>35.11 ft</em>
<em></em>
Step-by-step explanation:
This given situation can be thought of as triangle
where PQ is the length of pole.
PR is the length of rope.
and QR is the distance of bottom of pole to the point of fastening of rope to the ground.
And 
Given that:
PQ = 44 ft
PR = 51 ft

To find:
Side QR = ?
Solution:
We can apply Sine Rule here to find the unknown side.
Sine Rule:

Where
a is the side opposite to 
b is the side opposite to 
c is the side opposite to 

Now,

Let us use the Sine rule again:

So, the answer is <em>35.11 ft</em>.
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You've got five different problems in this photo ... four on top and the word problem on the bottom ... and they're all exactly the same thing: Taking two points and finding the slope of the line that goes through them.
In every case, the procedure is the same.
If the two points are (x₁ , y₁) and (x₂ , y₂) , then
the slope of the line that goes through them is
Slope = (y₂ - y₁) / (x₂ - x₁) .
This is important, and you should memorize it.
#1). (8, 10) and (-7, 14)
Slope = (14 - 10) / (-7 - 8) = 4 / -15
#2). (-3, 1) and (-17, 2)
Slope = (2 - 1) / (-17 - -3) = (2 - 1) / (-17 + 3) = 1 / -14
#3). (-20, -4) and (-12, -10)
Slope = [ -10 - (-4) ] / [ -12 - (-20) ]
=========================================
The word problem:
This question only gives you one point on the graph,
and then it wants to know what's the slope ?
What are you going to do for another point ?
A "proportional relationship" always passes through the origin,
so another point on the line is (0, 0) .
Now you have two points on THAT line too, and you can easily
find its slope.
The probability is 0.8997.
We will use a z-score to answer this question. z-scores are given by the formula

With our information, we have

Looking this up in a z-table (http://www.z-table.com) we see that the area to the left of this (everything less than, up to this value) is 0.8997.
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