2. There is a pine tree that may be too close to Jamal's house. He can't physically measure the tree, but he thinks it may hit his house someday. He is 6 feet tall and has a shadow that is 4 feet. At the same time of day, the tree casts a shadow that is 28 feet. a. Draw and label a picture to represent this scenario. Using the measurements, determine the height of the tree. b. If the base of the tree is 80 feet from the house, will it hit the house if it falls? Justify your answer.

Sure, let's tackle Jamal's pine tree problem step by step. --- ### **Problem Summary:** - **Jamal's Height:** 6 feet - **Jamal's Shadow:** 4 feet - **Tree's Shadow:** 28 feet - **Distance from Tree to House:** 80 feet --- ### **Part a: Determine the Height of the Tree** #### **1. Diagram Representation:** Since I can't draw the diagram here, I'll describe it so you can visualize or sketch it yourself: - **Triangles Involved:** - **Jamal's Triangle:** Represents Jamal and his shadow. - **Height:** 6 feet (vertical) - **Shadow Length:** 4 feet (horizontal) - **Tree's Triangle:** Represents the pine tree and its shadow. - **Height:** Unknown (let's denote it as *h*) - **Shadow Length:** 28 feet (horizontal) - **Labeling:** - Both triangles share the same angle of elevation from the ground to the sun, making them **similar triangles**. #### **2. Using Similar Triangles to Find the Tree's Height:** Since the triangles are similar, the ratios of corresponding sides are equal. \[ \frac{\text{Height of Jamal}}{\text{Shadow of Jamal}} = \frac{\text{Height of Tree}}{\text{Shadow of Tree}} \] Plugging in the known values: \[ \frac{6\, \text{ft}}{4\, \text{ft}} = \frac{h}{28\, \text{ft}} \] **Solve for *h*:** \[ h = \frac{6\, \text{ft} \times 28\, \text{ft}}{4\, \text{ft}} = \frac{168\, \text{ft}^2}{4\, \text{ft}} = 42\, \text{ft} \] **Therefore, the height of the pine tree is **42 feet**.** --- ### **Part b: Will the Tree Hit the House if it Falls?** #### **Given:** - **Height of Tree (from Part a):** 42 feet - **Distance from Tree to House:** 80 feet #### **Analysis:** When the tree falls towards the house, the **maximum horizontal distance** it can cover is equal to its height (assuming it falls perfectly horizontally). - **Maximum Reach of the Tree:** 42 feet - **Distance to House:** 80 feet #### **Conclusion:** Since the **maximum reach of the tree (42 feet)** is **less than the distance to the house (80 feet)**, the tree **will not** reach or hit the house if it falls towards it. --- ### **Final Answers:** **a.** The pine tree is **42 feet** tall. **b.** No, the tree will **not** hit the house if it falls. Its maximum reach of 42 feet is **less than** the 80 feet distance to the house.