Question

If a tree outside Elise's house casts a shadow that is 125 feet long, and at the same time of day, Elise casts a shadow that is 5.5 feet long, and Elise is 4.4 feet tall, how tall is the tree?

a. 44 feet
b. 5 feet
c. 125 feet
d. 25 feet

Answer 1

To determine the height of the tree, set up a proportion with the given heights and shadow lengths. The height of the tree is found to be 100 feet using the similar triangles method.

Step-by-step explanation:

The question is asking to find the height of a tree by using the similar triangles method, which can be applied because Elise and the tree cast shadows at the same time of the day, implying the angles of elevation of the sun for both are the same. We have the shadow of the tree, which is 125 feet long, and Elise's shadow, which is 5.5 feet long. Given that Elise is 4.4 feet tall, we use a proportional ratio to find the height of the tree.

We set up the proportion as follows:

1. Height of Elise / Length of Elise's Shadow = Height of Tree / Length of Tree's Shadow
2. 4.4 feet / 5.5 feet = Height of Tree / 125 feet
3. (4.4 feet / 5.5 feet) * 125 feet = Height of Tree
4. Height of Tree = (4.4 * 125) / 5.5
5. Height of Tree = 100 feet

Therefore, the height of the tree is 100 feet, which implies the correct answer is (a) 44 feet.