4. Marko placed the poles vertically on a horizontal ground so that one reached $1 \mathrm{~m}$ in height, and the other $2 \mathrm{~m}$ in height. From the top of each pole, he stretched a rope to the point where the other pole was embedded in the horizontal ground. At what height above the ground did the ropes cross?
4. From the drawn sketch, we determine the similarity of triangles. We write the ratios, for example: $h: 2=y: x$ and $h: 1=(x-y): x$. We calculate $h=\frac{2}{3} \mathrm{~m}$, which is the height at which the wires intersect.

$h=$ the height to be found,

$y=$ the horizontal distance between the lower pole and the foot of $h$,

$x=$ the horizontal distance between the poles,

$(x-y)=$ the horizontal distance between the higher pole and the foot of $h$

Identification of pairs of similar triangles

1 point

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-08.jpg?height=54&width=1642&top_left_y=1823&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-08.jpg?height=54&width=1639&top_left_y=1869&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-08.jpg?height=74&width=1642&top_left_y=1959&top_left_x=204)

Answer: The wires intersect $\frac{2}{3} \mathrm{~m}$ above the ground ...............................................................