125. Knowing the height of the candle, the height of the gnomon (vertical pole) and the distance between their bases, find the length of the shadow cast by the gnomon.
125. From the similarity of triangles (Fig. 37) we have:

$$
\frac{x}{x+d}=\frac{h}{H}, \text { hence } x=\frac{h d}{H-h}
$$

![](https://cdn.mathpix.com/cropped/2024_05_21_926f0bb262c8f9569516g-106.jpg?height=303&width=517&top_left_y=1048&top_left_x=358)

Fig. 37.

![](https://cdn.mathpix.com/cropped/2024_05_21_926f0bb262c8f9569516g-106.jpg?height=343&width=808&top_left_y=1028&top_left_x=904)

Fig. 38.