3. Two trees of heights 5 and 10 meters are at equal distances from a streetlight pole. These two trees cast shadows of lengths 5 and 15 meters. How tall is the pole?
3. Let $d$ be the distance from the tree to the flag, and $h$ the height of the flag. We have $h:(d+5)=5: 5$ and $h:(d+15)=10: 15$. Therefore, $d+5=h$ and $d+15=\frac{3}{2} h$, so we get $h+10=\frac{3}{2} h$ and $h=20$. Thus,

![](https://cdn.mathpix.com/cropped/2024_06_04_adcebcbe7d41887b6eefg-33.jpg?height=272&width=272&top_left_y=186&top_left_x=806)
the flag is 20 meters high.

![](https://cdn.mathpix.com/cropped/2024_06_04_adcebcbe7d41887b6eefg-33.jpg?height=269&width=372&top_left_y=190&top_left_x=1131)

Op 2019 2B 3