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Warm Up Solve each proportion.

9 27. 3 5. 6 x. x 3.5. x 75. 2.4 8. x 6. 8 7. =. =. =. =. Warm Up Solve each proportion. 1. 2. x = 45. x = 20. 3. 4. x = 4. x = 2. Copy in your spiral. Essential Question: How do you find an unknown value by using indirect measurement? Spi: 706.4.1.

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Warm Up Solve each proportion.

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  1. 9 27 3 5 6 x x 3.5 x 75 2.4 8 x 6 8 7 = = = = Warm Up Solve each proportion. 1. 2. x = 45 x = 20 3. 4. x = 4 x = 2

  2. Copy in your spiral Essential Question: How do you find an unknown value by using indirect measurement? Spi: 706.4.1

  3. Copy in your spiral Vocabulary indirect measurement Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.

  4. F B 9 ft 3 ft A C 4 ft G E x Additional Example 1: Geography Application Copy in your spiral Triangles ABC and EFG are similar. Find the length of side EG. Triangles ABC and EFG are similar.

  5. EF 36 9 3 EG x AB 3x 3 AC 3 4 Additional Example 1 Continued Copy in your spiral Triangles ABC and EFG are similar. Find the length of side EG. = Set up a proportion. Substitute 3 for AB, 4 for AC, and 9 for EF. = 3x = 36 Find the cross products. = Divide both sides by 3. x = 12 The length of side EG is 12 ft.

  6. H x E 7 in 8 in D F I G Check It Out: Example 1 Triangles DEF and GHI are similar. Find the length of side HI. 2 in Triangles DEF and GHI are similar.

  7. GH 56 8 2 HI x DE 2x 2 2 7 EF Check It Out: Example 1 Continued Triangles DEF and GHI are similar. Find the length of side HI. = Set up a proportion. Substitute 2 for DE, 7 for EF, and 8 for GH. = 2x = 56 Find the cross products. = Divide both sides by 2. x = 28 The length of side HI is 28 in.

  8. Indirect Measurement video

  9. 1 Understand the Problem Additional Example 2: Problem Solving Application Copy in your spiral A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree? The answer is the height of the tree. List the important information: • The length of the building’s shadow is 75 ft. • The height of the building is 30 ft. • The length of the tree’s shadow is 35 ft.

  10. 3 Solve Make a Plan 30 feet 35 feet 75 feet 2 Additional Example 2 Continued Use the information to draw a diagram. h Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

  11. 3 Solve 1050 75 75h 75 Additional Example 2 Continued 30 75 h 35 Corresponding sides of similar figures are proportional. = 75h = 1050 Find the cross products. = Divide both sides by 75. h = 14 The height of the tree is 14 feet.

  12. 4 Additional Example 2 Continued Look Back 75 30 Since = 2.5, the building’s shadow is 2.5 times its height. So, the tree’s shadow should also be 2.5 times its height and 2.5 of 14 is 35 feet.

  13. 1 Understand the Problem Check It Out: Example 2 A 24-ft building casts a shadow that is 8 ft long. A nearby tree casts a shadow that is 3 ft long. How tall is the tree? The answer is the height of the tree. List the important information: • The length of the building’s shadow is 8 ft. • The height of the building is 24 ft. • The length of the tree’s shadow is 3 ft.

  14. 3 Solve Make a Plan 24 feet 3 feet 8 feet 2 Check It Out: Example 2 Continued Use the information to draw a diagram. h Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.

  15. 3 Solve 8h 8 72 8 Check It Out: Example 2 Continued 24 8 h 3 Corresponding sides of similar figures are proportional. = 72 = 8h Find the cross products. = Divide both sides by 8. 9 = h The height of the tree is 9 feet.

  16. 4 Check It Out: Example 2 Continued Look Back 8 24 1 3 Since = , the building’s shadow is times its height. So, the tree’s shadow should also be times its height and of 9 is 3 feet. 1 3 1 3 1 3

  17. w 5 m 7 m 5.7 m Lesson Quiz 1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river? 2. A yardstick casts a 2-ft shadow. At the same time, a tree casts a shadow that is 6 ft long. How tall is the tree? 7.98 m 9 ft

  18. Tree = 3.3 m Park to House = 15 m. You need to add the missing value (10) and the distance from red-light to park (5).

  19. 21 ft 200 ft 37.5 m 13.5 m 4.2ft 103.3 ft

  20. There are 2 ways to solve #15. Either turn everything into inches first, then go back to feet or plug in the answers in the proportion and see which fractions are closest to each other.

  21. Use Indirect Measurement • MAPS In the figure, ΔGHK ∼ ΔJIK. Find the distance across the forest. 48 mi

  22. Homework: • Worksheet practice 11-6

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