An 8 ft tall pole casts a shadow that is 9 ft long. At the same time, a lawn omament casts a shadow that is 2 ft long. How tall is the lawn omam ound to the nearest tenth. Irnament height \( = \)

To find the height of the lawn ornament, we can use the concept of similar triangles. The ratio of the height of the pole to its shadow length is the same as the height of the ornament to its shadow. So we set it up like this: \(\frac{8 ft}{9 ft} = \frac{x}{2 ft}\). Cross-multiplying gives us \(8 ft \cdot 2 ft = 9 ft \cdot x\), or \(16 = 9x\). Dividing both sides by 9, we find \(x ≈ 1.8 ft\). Rounded to the nearest tenth, the lawn ornament height is 1.8 ft! Now, let’s think about the concept of proportional shadows. When the sun's rays hit objects at the same angle, they create similar triangles. This means that no matter the size of your objects, the shadows will always reflect their heights proportionally as long as the light source remains consistent. That’s why this method works!