1. Justin is 74 inches tall and casts a shadow that is 102inches long. At the same time, a tree casts a shadow thatis 39 feet long. How tall is the tree to the nearest foot?

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5. Catie is trying to determine the height that a ladder reaches as it leans against a wall. She walks under the ladder and touches her forehead to it as shown. If her feet are 16 inches from the ladder's base, the ladder's base is 4.5 feet from the bottom of the wall, and Catie is 5 feet 6 inches tall, then come up with an estimate for how high the ladder reaches up the wall to the nearest tenth of a foot. Watch your units on this problem and show all work. REASONING 7. A line is drawn on a coordinate grid to the right. It has the points A, B, and Clabeled as shown with coordinates A(0, 3), B(3,5) and C(12,11). Right triangles are drawn using points D and E. (a) Segments AD and BE are parallel because they are both horizontal. What does this tell you about ZBAD and ZCBE? Explain. 6. What might be some factors that would cause error in your estimate in problem #6? List as many as you can. (b) Why must ABAD be similar to ACBE? (c) Find the slope of AB and BC below. Show your slope calculations. Slope of AB: 16 in Slope of BC: 4.5 ft 5 ft 6 in (d) Given your answer to (b), why does it now make sense that the two slopes in (c) are equal? x 5. Catie is trying to determine the height that a ladder reaches as it leans against a wall. She walks under the ladder and touches her forehead to it as shown. If her feet are 16 inches from the ladder's base, the ladder's base is 4.5 feet from the bottom of the wall, and Catie is 5 feet 6 inches tall, then come up with an estimate for how high the ladder reaches up the wall to the nearest tenth of a foot. Watch your units on this problem and show all work. REASONING 7. A line is drawn on a coordinate grid to the right. It has the points A, B, and Clabeled as shown with coordinates A(0, 3), B(3,5) and C(12,11). Right triangles are drawn using points D and E. (a) Segments AD and BE are parallel because they are both horizontal. What does this tell you about ZBAD and ZCBE? Explain. 6. What might be some factors that would cause error in your estimate in problem #6? List as many as you can. (b) Why must ABAD be similar to ACBE? (c) Find the slope of AB and BC below. Show your slope calculations. Slope of AB: 16 in Slope of BC: 4.5 ft 5 ft 6 in (d) Given your answer to (b), why does it now make sense that the two slopes in (c) are equal? x