A mast

The wind broke a mast 32 meters high so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part, and the ground form a rectangular triangle. At what height was the mast broken?

Correct answer:

x =  12 m

Step-by-step explanation:

$$\begin{gathered} c^2=x^2+16^2 \\ x+c=32 \\ (32-x{)}^2=x^2+16^2 \\ 32^2-2\cdot 32\cdot x=16^2 \\ x=(32^2-16^2)/(2\cdot 32)=12 \\ c=32-x=32-12=20 \\ x=12=12\text{m} \end{gathered}$$

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