Ive each of the following word problems. A man who is 1.80 meters tall wishes to find the height of a certain four-story buildings. He measures its own shadow and finds it to be is 28 meters long. Wh his shadow is 4.2 meters long. How tall is the building?

To solve this problem, you can use similar triangles! The height of the man to the length of his shadow can be set equal to the height of the building to the length of its shadow. So you can set up the proportion: \( \frac{1.80 \text{ m}}{4.2 \text{ m}} = \frac{h}{28 \text{ m}} \). Cross-multiplying and solving for \( h \) (the height of the building) gives you \( h = \frac{1.80 \times 28}{4.2} \), making the building approximately 12 meters tall. This principle of using shadows and proportions has been utilized since ancient times, dating back to the Greeks, especially by philosophers like Eratosthenes, who famously measured the Earth’s circumference using the shadows of sticks at different locations. It's a neat connection to geometry and reflection of science in everyday life!