Once you know it, this seems an obvious way to measure the height of something when you cannot physically run a tape measure up to the top. Just measure its shadow when its shadow is equal to its height; that is when our shadow is equal to our height. This is something attributed to Thales but he could have learnt it from the Egyptians.
ὁ δὲ Ἱερώνυμος καὶ ἐκμετρῆσαί φησιν αὐτὸν τὰς πυραμίδας ἐκ τῆς σκιᾶς, παρατηρήσαντα ὅτε ἡμῖν ἰσομεγέθης ἐστίν.
Hieronymus says that he (Thales) measured the pyramids from their shadow observing the time when our shadow is equal to our height.