Question

How high is a tree that casts a 26 ft shadow at the same time a 6 ft pole casts a shadow which is 13 ft.

Is it 12 ft

Answer 1

To determine the height of the tree, we can use the concept of similar triangles. By setting up a proportion between the height of the tree and the height of the pole, we can solve for the height of the tree. The height of the tree is found to be 12 ft.

Step-by-step explanation:

To determine the height of the tree, we can use the concept of similar triangles. The height of the tree is related to the height of the pole and their respective shadows. Let's denote the height of the tree as h and the height of the pole as p. We can set up the following proportions:

h / 26 = p / 13

Given that the height of the pole is 6 ft and its shadow is 13 ft, we can substitute the values into the proportion:

h / 26 = 6 / 13

Cross-multiplying, we get:

h = (6 * 26) / 13

Simplifying further:

h = 12 ft

The height of the tree is indeed 12 ft.