Question

A fence post that is 5 feet tall casts a 2-foot shadow at the same time that a tree that is 27 feet tall casts a shadow in the same direction. Determine the length of the tree's shadow.

8.5 feet
10.8 feet
12 feet
21.4 feet

Answer 1

We can use the property of similar triangles to solve this problem. The triangles formed by the tree, its shadow, the fence post, and its shadow are similar. Let's call the length of the tree's shadow "x". Then we can set up the following proportion:

(tree height) / (tree shadow length) = (fence post height) / (fence post shadow length)

Plugging in the given values, we get:

27 / x = 5 / 2

Cross-multiplying, we get:

27 * 2 = 5 * x

Simplifying, we get:

54 = 5x

Dividing both sides by 5, we get:

x = 10.8

Therefore, the length of the tree's shadow is 10.8 feet. Answer: (B) 10.8 feet.