The height of the pole is 96 feet
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]
[tex]a^{2}+b^{2}=c^{2},[/tex]
Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.
Set up the equation [tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex] using the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]).
[tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex]
On simplifying we get
[tex]h^2+h^2-136h+4624 = h^2+8h+16[/tex]
[tex]2h^2-136h+4624=h^2+8h+16[/tex]
[tex]h^2-144h+4608=0[/tex]
Solving using quadratic formula
[tex]h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}[/tex]
[tex]h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}[/tex]
h1 = 96 feet , h2 = 48 feet
If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .
Hence the height of the pole is 96 feet
Learn more about Pythagoras theorem here :
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