5 -7 Indirect Measurement Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
5 -7 Indirect Measurement Warm Up Solve each proportion. 1. 3. x = 45 2. x = 20 x=2 4. x=4
5 -7 Indirect Measurement Problem of the Day A plane figure is dilated and gets 50% larger. What scale factor should you use to dilate the figure back to its original size? (Hint: The answer is not 1. ) 2 2 3
5 -7 Indirect Measurement Sunshine State Standards MA. 8. G. 2. 1 Use similar triangles to solve problems that include height and distances.
5 -7 Indirect Measurement Vocabulary indirect measurement
5 -7 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.
5 -7 Indirect Measurement Additional Example 1: Geography Application Triangles ABC and EFG are similar. Find the length of side EG. F B 9 ft 3 ft A 4 ft C E x Triangles ABC and EFG are similar. G
5 -7 Indirect Measurement Additional Example 1 Continued Triangles ABC and EFG are similar. Find the length of side EG. AB = EF AC EG Set up a proportion. 3 = 9 4 x Substitute 3 for AB, 4 for AC, and 9 for EF. 3 x = 36 Find the cross products. 3 x = 36 Divide both sides by 3. 3 3 x = 12 The length of side EG is 12 ft.
5 -7 Indirect Measurement Check It Out: Example 1 The triangles are similar. Find the distance across the river.
5 -7 Indirect Measurement Check It Out: Example 1 Continued The triangles are similar. Find the distance across the river. x = 4 ; 3 x = 36; 9 3 x = 36 = 12 3 The distance across the river is 12 meters.
5 -7 Indirect Measurement Additional Example 2: Problem Solving Application 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? 1 Understand the Problem 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.
5 -7 Indirect Measurement Additional Example 2 Continued 2 Make a Plan Use the information to draw a diagram. h 30 feet 35 feet 3 75 feet Solve Draw dashed lines to form triangles. The building with its shadow and the tree with its shadow form similar right triangles.
5 -7 Indirect Measurement Additional Example 2 Continued 3 Solve 30 = h 75 35 Corresponding sides of similar figures are proportional. 75 h = 1050 Find the cross products. 75 h = 1050 75 75 Divide both sides by 75. h = 14 The height of the tree is 14 feet.
5 -7 Indirect Measurement Additional Example 2 Continued 4 Look Back 75 Since 30 = 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.
5 -7 Indirect Measurement Check It Out: Example 2 A 5 -ft tall student casts a shadow that is 7 ft long. A nearby light pole casts a shadow that is 21 ft long. How tall is the light pole? x ft 21 ft 5 ft 7 ft
5 -7 Indirect Measurement Check It Out: Example 2 Continued x = 5 21 7 7 x = 105 x = 15 The light pole is 15 feet tall.
5 -7 Indirect Measurement Lesson Quizzes Standard Lesson Quiz for Student Response Systems
5 -7 Indirect Measurement 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. The triangles in the diagram are similar How wide is the river? 7. 98 m w 5 m 7 m 5. 7 m 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? 9 ft
5 -7 Indirect Measurement Lesson Quiz for Student Response Systems 1. Dane wants to know the width of the pond in the field. He drew a diagram and labeled it with his measurements. The triangles in the diagrams are similar. How wide is the pond? A. 100 yd B. 96 yd C. 92 yd D. 80 yd
5 -7 Indirect Measurement Lesson Quiz for Student Response Systems 2. An apartment building that is 51 feet tall casts a 90 foot shadow. At the same time, a tree casts a shadow that is 48 feet long. How tall is the tree? A. 27. 2 ft B. 39 ft C. 42 ft D. 50 ft
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