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Mathematics > Standard Multiple Choice

Miguel is centimeters tall. At 2:00 p.m. one day, his shadow is centimeters long, and the shadow of a nearby fence post is centimeters long. In terms of , what is the height, in centimeters, of the fence post?

# Correct!

### Explanation

The situation described in the question can be pictured as in the figure below, where is the height, in centimeters, of the fence post.

There are two right triangles in the figure. One triangle is formed by part of the line from the sun to point , the perpendicular from Miguel’s head to the ground, and Miguel’s shadow along the ground. The other triangle is formed by part of the line from the sun to point , the perpendicular from the top of the fence post to the ground, and the fence post’s shadow along the ground. Since these two right triangles share the acute angle at , they are similar triangles. Since the corresponding sides of similar triangles are in proportion, it follows that. Solving this equation for , the height, in centimeters, of the fence post, yields .