A piece of bamboo is 32 feet tall (assume the bamboo is standing at a 90 degree angle). A strong gust of wind breaks the bamboo at a certain point. The original top of the bamboo stalk falls to the ground at a distance of 16 feet from the base of the plant, while the plant is still barely connected at the point of the break. At what height from the ground was the bamboo broken?

Question

A piece of bamboo is 32 feet tall (assume the bamboo is standing at a 90 degree angle). A strong gust of wind breaks the bamboo at a certain point. The original top of the bamboo stalk falls to the ground at a distance of 16 feet from the base of the plant, while the plant is still barely connected at the point of the break. At what height from the ground was the bamboo broken?

Answer 1

Let's assume that the height at which the bamboo was broken is x.

Since the original top of the bamboo stalk falls to the ground at a distance of 16 feet from the base of the plant, and the bamboo is still barely connected at the point of the break, the remaining part of the bamboo is (32 - x) feet tall.

Now, we can set up a proportion using the similar triangles formed by the fallen part of the bamboo and the remaining part of the bamboo:

(32 - x) / x = 16 / (32 - 16)

Simplifying the proportion:
(32 - x) / x = 16 / 16
(32 - x) / x = 1

Cross multiplying, we get:
32 - x = x
32 = 2x
x = 32 / 2
x = 16

Therefore, the bamboo was broken at a height of 16 feet from the ground.