Answer:
[tex]12\sqrt{3} [/tex] feet
Step-by-step explanation:
In a 30-60-90 triangle, the ratios of the side lengths of the triangle is [tex]1:\sqrt{3} :2[/tex]
Where 1 is the shortest leg, root(3) is the longer leg, and 2 is the hypotenuse.
First we can set x equals to the length of the original pole, and so the shorter leg has a length of x/3 and using the ratio of side lengths, we can find that:
[tex]\frac{x}{3} * \sqrt{3} = \frac{\sqrt{3} x}{3} = 12[/tex]
Solving for x, we find that
[tex]x=\frac{36}{\sqrt{3} } = \frac{36 * \sqrt{3} }{\sqrt{3} * \sqrt{3} } = \frac{36 \sqrt{3} }{3} = 12\sqrt{3} [/tex]
So the length of the original pole would be [tex]12\sqrt{3} [/tex] feet
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