SOLUTION: A flagpole is secured on opposite sides by two guy wires, each of which is 7 ft longer than the pole. The distance between the points where the wires are fixed to the ground is equ

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Question 156496: A flagpole is secured on opposite sides by two guy wires, each of which is 7 ft longer than the pole. The distance between the points where the wires are fixed to the ground is equal to the length of one guy wire. How tall is the flagpole? (to the nearest inch)
I have no idea how to solve this :(
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Think...right triangles!
The flag pole can be represented by the height of the right triangle, one of the guy wires can be represented by the hypotenuse of the right triangle, and the distance from the anchor point of one of the guy wires to the base of the flag pole can be represented by the base of the right triangle.
Now think about the Pythagorean theorem!
c%5E2+=+a%5E2%2Bb%5E2 where c = the length of the hypotenuse (guy wire) = a+7, a = the height of the flag pole, and b = the length of the base (half of the length of one guy wire).
Let's see what all the measurements are:
c = the length of one guy wire = the height of the flag pole plus 7 ft.
a = the height of the flag pole and this is what we are trying to find.
b = half the length of one guy wire = (a+7)/2
So we'll make the appropriate substitutions into the formula and evaluate it.
%28a%2B7%29%5E2+=+a%5E2+%2B+%28%28a%2B7%29%2F2%29%5E2 Simplifying this, we get...
a%5E2%2B14a%2B49+=+a%5E2%2B%28a%5E2%2B14a%2B49%29%2F4 Subtract a%5E2from both sides.
14a%2B49+=+%28a%5E2%2B14a%2B49%29%2F4 Multiply through by 4 to clear the fraction.
56a%2B196+=+a%5E2%2B14a%2B49 Subtract 56a from both sides.
196+=+a%5E2-42a%2B49 Subtract 196 from both sides.
a%5E2-42a-147+=+0 Use the quadratic formula to solve:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a Here, a = 1, b = -42, and c = -147. Change the variable from x to a.
a+=+%28-%28-42%29%2B-sqrt%28%28-42%29%5E2-4%281%29%28-147%29%29%29%2F2%281%29
a+=+%2842%2B-sqrt%281764-%28-588%29%29%29%2F2
a+=+%2842%2B-sqrt%282352%29%29%2F2
a+=+45.25 or a+=+-3.25 Discard the negative solution as the flag pole height is a positive value.
The flag pole is 45.25 feet or 543 inches.