Question

On a sunny day, a 6-foot tall woman positions herself so that her shadow lines up with the end of the shadow of a pine tree. The woman's shadow is 8 feet long, and she is standing 12 feet from the base of the pine tree, as shown below. Based on the information provided in the diagram, describe how to solve for , the height of the pine tree

Answer 1

The problem can be solved by setting up a proportion using similar triangles, comparing the woman's height to her shadow, and the pine tree's height to the total length of the woman's shadow plus the distance to the tree. By cross-multiplying and solving for 'h', we find that the pine tree's height is 15 feet.

Step-by-step explanation:

The problem provided can be solved using the principles of similar triangles. The woman's height and the length of her shadow, along with the distance to the pine tree, set up proportions with the unknown height of the pine tree and the combined length of the woman's shadow and the distance from her to the tree. Using the fact that the ratios of corresponding sides of similar triangles are equal, we can set up the following proportion:

Woman's height / Woman's shadow length = Pine tree's height / (Woman's shadow length + Distance to pine tree)

This is:

6 ft / 8 ft = h / (8 ft + 12 ft)

We can solve for h, the pine tree's height, by cross-multiplying and solving the resulting equation:

6 ft / 8 ft = h / 20 ft

6 ft × 20 ft = 8 ft × h

120 ft² = 8h ft

h = 120 ft² / 8 ft

h = 15 feet

Therefore, the height of the pine tree is 15 feet.