Final answer:
To find the height of a tree that casts a 27-ft shadow when a 7-ft post casts a 14-ft shadow, we use the ratio of the post height to its shadow, which is equivalent to the tree height to its shadow, resulting in the tree being 13.5 feet tall.
Step-by-step explanation:
To determine how high a tree is that casts a 27-ft shadow when a 7-ft post casts a 14-ft long shadow, we can use the concept of similar triangles. The ratio of the height of the post to its shadow length is the same as the ratio of the height of the tree to its shadow length. Therefore, the proportion is as follows:
Height of post / Shadow of post = Height of tree / Shadow of tree
7 ft / 14 ft = Height of tree / 27 ft
To solve for the height of the tree, we cross-multiply and divide:
Height of tree = (7 ft / 14 ft) * 27 ft
Height of tree = (1/2) * 27 ft
Height of tree = 13.5 ft
The tree is 13.5 feet tall.