There is an interesting gemara in Meseches Eruvim 43b (translation from The William Davidson digital edition of the Koren Noe Talmud Bavli):

Rashi makes the following comment (translation from the Soncino English Translation of the Babylonian Talmud, Tractate Erubin by Rabbi Dr. Isidore Epstein in 1935):

“Having ascertained beforehand the distance his tube commands, he takes up a position from which he can just see the bottom of the ravine, and by subtracting the distance between the brink of the ravine and his position from the distance the tube commands, he obtains the depth of the ravine.”

It is fascinating, as a physics teacher, to see mathematics used like this in the Talmud. To further understand Rashi’s method, I have done a rough calculation using modern trigonometry (photograph of work done by the author) as to how Rabban Gamaliel’s “tube” might have operated:

I apologize for the crude drawings, but the rough calculation on the photo I took, shows how one can start at the edge of the ravine, take a reading, and then walk backwards until one can just barely see the bottom of the ravine. If you are not into mathematics, then you can still appreciate the knowledge the sages employed, especially when determining the position of the moon for the announcement, by the Sanhedrin, of the new month (Rosh Chodesh).