Question

At certain times of the day, shadows form similar triangles. Use this information, and the information below, to determine the unknown height, x, of the tree: 12.5, 12.5, 3.2, 3.2, 17.5, 17.5, 10, 10, 20.1, 20.1.

Answer 1

To determine the unknown height of the tree using similar triangles and a proportion, set up the equation: 12.5 inches / 12.5 feet = x inches / 3.2 feet. By cross-multiplying and solving for x, the height of the tree is found to be 3.2 inches.

Step-by-step explanation:

To determine the unknown height of the tree, we can use the concept of similar triangles. Given the information provided, we can set up a proportion using the corresponding sides of the similar triangles.

Let the height of the tree be x inches and the height of the shadow be 12.5 inches. From the given information, we can set up the proportion:

12.5 inches / 12.5 feet = x inches / 3.2 feet

By cross-multiplying, we can solve for x:

(12.5 inches * 3.2 feet) / 12.5 feet = x inches

Simplifying the expression, we find that the unknown height of the tree, x, is equal to 3.2 inches.