A mast

A mast 32 meters high was broken by the wind 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?

Result

x =  12 m

Solution:

c2=x2+162 x+c=32 (32−x)2=x2+162 322−2⋅ 32⋅ x=162 x=(322−162)/(2⋅ 32)=12 c=32−x=32−12=20 x=12 mc^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 \ \text{m}

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