Question

a telephone pole needs a wire attached to its top and anchored to the ground at a point that is 56 feet less than the height of the pole. if the wire is to be 16 feet longer than the height of the pole what is the height of the pole

Answer 1

check the picture below.


`\bf (y+16)^2=(y-56)^2+y^2 \\\\\\ \underline{y^2}+32y+16^2=y^2-112y+56^2+\underline{y^2} \\\\\\ 32y+256=y^2-112y+3136\implies 0=y^2-144y+2880 \\\\\\ 0=(y-24)(y-120)\implies y= \begin{cases} \boxed{120}\\ 24 \end{cases}`


it cannot be 24, because then the ground base area will be 24 - 56, which is a negative amount and unfeasible for the phenomena.