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Unit 6: Scale Factor and Measurement How will you measure up? What am I Learning Today? Indirect Measurement How will I show that I learned it? Demonstrate the relationship between similar plane figures using ratio and proportion Use proportions and similar figures to find unknown measures Solve real world problems using indirect measurement Do you know how tall the Eiffel Tower is? Is there a way to find out without actually measuring it? What I do know is that on a sunny day, its shadow is 328 feet long. What could we do to solve this problem? What ideas do you have for determining its height? Questions Answers What is indirect measurement? A technique that uses proportions to find a measurement when it is not possible to measure something directly. How can I find the length or height without using standard measuring tools? Use similar figures and proportions: 1) Draw a sketch to identify similarities 2) Create a proportion substituting values for the given measurements 3) Solve for X Use the similar triangles to find the height of the tree. 6 3 __ __ = h 9 Write a proportion using corresponding sides. h • 3 = 6 • 9 The cross products are equal. 3h = 54 3h 54 ___ ___ 3 = 3 h is multiplied by 3. Divide both sides by 3 to undo multiplication. h = 18 The tree is 18 feet tall. 6 ft. h 3 ft. 9 ft. Measurement Application A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket? h 91.5 Write a proportion using __ ____ = corresponding sides. 4 3 4 • 91.5 = h • 3 The cross products are equal. 366 = 3h h is multiplied by 3. 366 = ___ 3h Divide both sides by ___ 3 to undo 3 3 multiplication. 122 = h The rocket is 122 feet tall. 1. Use the similar triangles to find the height of the post. x 20 feet 8 ft 15 ft 6 ft 2. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost? 25 feet 3. A stop sign casts a shadow 8 meters long, while a bush nearby casts a shadow 4.5 meters long. If the stop sign is 3.2 meters high, how tall is the bush? 1.8 meters Measuring the Oddities of America Measure your height to the nearest quarter inch Measure your shadow to the nearest quarter inch Using this information, determine the heights or shadow lengths of the following large immeasurable objects Create proportions and solve for the missing piece of information The Jolly Green Giant This monument found in Blue Earth, Minnesota stands a proud 55 feet tall. Using your height and shadow length, find the length of the Jolly Green Giant’s shadow? The World’s Tallest Man Robert Pershing Wadlow was (and still is) the tallest human being ever recorded. He reached 8' 11" (272 cm) in height and 490 pounds (222.26 kg) in weight before his death at the age of 22. What would have been the length of his shadow compared to yours? World’s Tallest Snow Woman Built in Bethel, Maine, Olympia Snow Woman took 28 days and 13 million pounds of snow to construct. She has a shadow of 61 feet long. How tall is this snow woman? The World’s Tallest Arcade Game This arcade machine stands 13 feet tall, has a 70 inch screen, and plays vintage video games. It casts a shadow of 6.5 feet. If Ms. Atkinson is 5.167 feet tall, how long would her shadow be in comparison? Exit Ticket Draw a sketch to represent each problem. Set up the proportion and solve. Be sure to label your answer. A flagpole casts a shadow that is 9 feet. An office building casts a shadow that is 15 feet. If the building is 60 feet tall, how tall is the flagpole? An office building casts a 150-foot shadow at the same time a nearby pedestrian casts a 3foot shadow. If the pedestrian is 6 feet tall, how tall is the office building?