Diagram:
From the above right triangle, we can stablish the following:
[tex]\begin{gathered} pythagorean\text{ }theorem:a^2+b^2=c^2 \\ \left(x\right?^2+\left(x-17\right)^2=\left(x+1\right)^2 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} x^2+x^2-34x+289=x^2+2x+1 \\ x^2+x^2-x^2-34x-2x+289-1=0 \\ x^2-36x+288=0 \end{gathered}[/tex]apply the quadratic formula,
[tex]\begin{gathered} x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ x_{1,\:2}=\frac{-\left(-36\right)\pm \sqrt{\left(-36\right)^2-4\cdot \:1\cdot \:288}}{2\cdot \:1} \end{gathered}[/tex]then,
[tex]x_{1,\:2}=\frac{-\left(-36\right)\pm \:12}{2\cdot \:1}[/tex]separate the solutions,
[tex]x_1=\frac{-\left(-36\right)+12}{2\cdot \:1},\:x_2=\frac{-\left(-36\right)-12}{2\cdot \:1}[/tex]Thus,
[tex]x=24,\:x=12[/tex]since, the shadow is x-17 meters long, then any value below 17 does not make much sense, therefore,
The answer is, x = 24
