Question 10, 1,2.60 WW Eceres Casty, of i2 of to ponts Ponter off 1 A tree oasts a shadow 30 ft long. At the same time, the shadow cast by a vertical 5 -ff pole is 4 ff long. Find the height of the tree. The tree's height is \( \square \) f.

To solve this problem, you can use the concept of similar triangles. Since the sun’s rays create similar angles with both the tree and the pole, the ratios of their heights to their shadow lengths will be the same. Here’s the math: Let the height of the tree be \( h \) ft. Using the ratios, we have: \[ \frac{h}{30} = \frac{5}{4} \] Now, cross-multiply to solve for \( h \): \[ 4h = 150 \quad \Rightarrow \quad h = \frac{150}{4} = 37.5 \text{ ft} \] So, the height of the tree is \( 37.5 \) ft. To make this concept stick, think about how similar triangles show up everywhere—like when you look at buildings and their shadows or even in your backyard with your garden! Understanding proportions can really help visualize the relationships in everyday life. If you'd like to dive deeper into similar triangles, consider exploring geometry resources that relate to real-world applications, such as navigation or architecture. You'll be amazed at how often these principles come into play!