This is the 5699th most frequent Japanese word.
たけ
"たけ" (take) means "bamboo."
In this sentence, "たけ" is used to mean "height" or "altitude," referring to the measurement of the mountain's elevation.
山のたけが高いです。
The mountain's height is tall.
Here, "たけ" means "bamboo," referring to the plant species that grows in the mentioned location.
たけは竹林に生えています。
Bamboo grows in the bamboo grove.
In this context, "たけ" figuratively stands for "height" or "degree," indicating the extent of his enthusiasm.