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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!
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.
Simplifying this, we get...
from both sides.
Multiply through by 4 to clear the fraction.
Subtract 56a from both sides.
Subtract 196 from both sides.
Use the quadratic formula to solve:
Here, a = 1, b = -42, and c = -147. Change the variable from x to a.
Discard the negative solution as the flag pole height is a positive value.
The flag pole is 45.25 feet or 543 inches.