Indirect Measurement. 7-5 Write the correct answer. 1. Use similar triangles to find the height of the lamppost.
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1 Practice A Write the correct answer. 1. Use similar triangles to find the height of the lamppost. 2. Use similar triangles to find the height of the man. 3. A 3-foot-tall boy looks into a mirror at the county fair. The mirror makes a person appear shorter. The boy appears to be 1 foot tall in the mirror. If a man appears to be 2 feet tall in the mirror, what is his actual height? 5. A bicycle casts a shadow that is 8 feet long. At the same time, a girl who is 5 feet tall casts a shadow that is 10 feet long. How tall is the bicycle? 7. Through a magnifying glass, a 2-centimeter-long bug looks like it is 12 centimeters long. How long would a 3-centimeter bug look in that same magnifying glass? 4. On a sunny day, a carnation casts a shadow that is 20 inches long. At the same time, a 3-inch-tall tulip casts a shadow that is 12 inches long. How tall is the carnation? 6. A sand castle casts a shadow that is 5 inches long. A 15-inch-tall bucket sitting next to the sand castle casts a shadow that is 3 inches long. How tall is the sand castle? 8. In the late afternoon, a wagon casts a shadow that is 15 feet long. A boy pulling the wagon who is 4 feet tall casts a shadow that is 20 feet long. How tall is the wagon?
2 Practice B Write the correct answer. 1. Use similar triangles to find the height of the building. 2. Use similar triangles to find the height of the taller tree. 3. A lamppost casts a shadow that is 35 yards long. A 3-foot-tall mailbox casts a shadow that is 5 yards long. How tall is the lamppost? 5. A building casts a shadow that is 348 meters long. At the same time, a person who is 2 meters tall casts a shadow that is 6 meters long. How tall is the building? 7. In the early afternoon, a tree casts a shadow that is 2 feet long. A 4.2-foottall boy standing next to the tree casts a shadow that is 0.7 feet long. How tall is the tree? 4. A 6-foot-tall scarecrow in a farmer s field casts a shadow that is 21 feet long. A dog standing next to the scarecrow is 2 feet tall. How long is the dog s shadow? 6. On a sunny day, a tree casts a shadow that is 146 feet long. At the same time, a person who is 5.6 feet tall standing beside the tree casts a shadow that is 11.2 feet long. How tall is the tree? 8. Steve s pet parakeet is 100 mm tall. It casts a shadow that is 250 mm long. A cockatiel sitting next to the parakeet casts a shadow that is 450 mm long. How tall is the cockatiel?
3 Practice C Write the correct answer. 1. Use similar triangles to find the height of the tower. 2. Use similar triangles to find the height of the man. 3. On a sunny day, a 6.5-foot-tall ladder casts a shadow that is 19.5 feet long. A man who is 6.2 feet tall is painting next to the ladder. How long is his shadow? 5. Brian, who is twice as tall as Cole, is 6.5 feet tall. Cole casts a shadow that is feet long. If Brian is standing next to Cole, how long is Brian s shadow? 7. A mother giraffe is 18.7 feet tall. Her baby is 5.25 feet tall. The baby giraffe casts a shadow that is 35.7 feet long. How long is the mother giraffe s shadow? 4. A building casts a shadow that is 1,125 meters long. A woman standing next to the building casts a shadow that is 6.25 meters long. She is 2.5 meters tall. How tall is the building? 6. A 4.5-foot-tall boy stands so the top of his shadow is even with the top of a flagpole s shadow. If the flagpole s shadow is 34 feet long, and the boy is standing 25 feet away from the flagpole, how tall is the flagpole? 8. A shorter flagpole casts a shadow 15.3 feet shorter than the shadow of a longer pole. The taller pole is 26.5 feet tall and casts a shadow 47.7 feet long. How tall is the shorter pole?
4 Review for Mastery If you cannot measure a length directly, you can use indirect measurement. Indirect measurement uses similar figures and proportions to find lengths. The small tree is 8 feet high and it casts a 12-foot shadow. The large tree casts a 36-foot shadow. The triangles formed by the trees and the shadows are similar. So, their heights are proportional. To find the height of the large tree, first set up a proportion. Use a variable to stand for the height of the large tree. = Write a proportion using corresponding sides = 12 x The cross products are equal. 12x = 288 x is multiplied by x = 288 Divide both sides by x = 24 So, the height of the tall tree is 24 feet. Use indirect measurement to find the missing heights _
5 Challenge Mirror Measurements When it is noon, nighttime, a cloudy day, or when you are inside, there are hardly any shadows to use for indirect measurement. Instead, you can use mirrors to measure in the following way. Place a mirror on the floor. Move back until you see the reflection of the top of the object you want to measure in the mirror. This creates two similar triangles, as illustrated in the picture to the right. You can then use proportions to find the unknown height: h = h 3 = 5 6 3h = 30 3h = h = 10 So, the height of the classroom is 10 feet. Find the missing height in each drawing to the nearest whole foot _ 3. 4.
6 Problem Solving Write the correct answer. 1. The Taipei 101 in Taiwan was the tallest building in the world in On a sunny day, the Taipei 101 casts a shadow that is 5001 feet long. A 6-foot-tall person standing nearby casts an 18-foot-long shadow. How tall is the Taipei 101? 2. The Sears Tower in Chicago is the tallest building in the United States. On a sunny day, the Sears Tower casts a shadow that is 2,908 feet long. A 5-foot-tall person standing by the building casts a 10-foot-long shadow. How tall is the Sears Tower? 3. The world s tallest man cast a shadow that was 535 inches long. At the same time, a woman who was 5 feet 4 inches tall cast a shadow that was 320 inches long. How tall was the world s tallest man in feet and inches? Circle the letter of the correct answer. 5. An NFL goalpost casts a shadow that is 170 feet long. At the same time, a yardstick casts a shadow that is 51 feet long. How tall is an NFL goalpost? A 100 feet B 56 2/3 feet C 10 feet D 1 foot 7. A 6-foot-tall man casts a shadow that is 30 feet long. If a boy standing next to the man casts a shadow that is 12 feet long, how tall is the boy? A 2 feet B 2.2 feet C 2.4 feet D 5 feet 4. The Hoover Dam on the Colorado River casts a shadow that is 2,904 feet long. At the same time, an 18-foot-tall flagpole next to the dam casts a shadow that is 72 feet long. How tall is Hoover Dam? 6. A gorilla casts a shadow that is 600 centimeters long. A 92-centimeter-tall chimpanzee casts a shadow that is 276 centimeters long. What is the height of the gorilla in meters? F 0.2 meter G 2 meters H 20 meters J 200 meters 8. An ostrich is 108 inches tall. If its shadow is 162 inches, and an emu standing next to it casts a 90-inch shadow, how tall is the emu? F 60 inches H 162 inches G 90 inches J inches
7 Reading Strategies Following Procedures Indirect means not direct. We use indirect measurement when it is not possible to use standard measurement tools. Measuring the height of a very tall tree or water tower is difficult to do directly. An indirect method of measuring uses similar figures and proportions to find the length or height. These two triangles are similar. 1. What side of the second triangle corresponds to side AB? 2. What side of the second triangle corresponds to side AC? 3. What side of the second triangle corresponds to side BC? You can set up a proportion using two corresponding sides from each triangle to find the missing side. 4. Write a ratio using the lengths for sides AC and DF. 5. Write a ratio using the lengths for sides AB and DE. 6. Write the proportion for the two ratios above. 7. Write a ratio using the lengths for sides BC and EF. 8. Write a ratio using the lengths for sides AB and DE. 9. Write a proportion for the two ratios above.
8 Puzzles, Twisters & Teasers Not Quite the Same Solve the crossword. Unscramble the circled letters to answer the question. Down 1. In similar corresponding angles are congruent. 2. Figures that have the same shape but not necessarily the same size. 4. Solve: 5 30 = x To sum two numbers. 7. Six, fourteen, fifty-two, and seventy-eight are all numbers. Across 3. In similar figures, corresponding have lengths that are proportional. 5. Indirect 8. Solve: 6 x = A figure with three sides is a -angle. What do you use to make indirect measurements? FIGURES
9 Answers LESSON Practice A 1. h = 10 feet 2. h = 6 feet 3. 6 feet 4. 5 inches 5. 4 feet inches cm 8. 3 feet Practice B 1. h = 24 m 2. 5 meters feet 4. 7 feet meters feet feet millimeters Practice C 1. h = yd 2. h = 5.4 feet feet meters feet feet feet feet Review for Mastery feet 2. 6 feet CODE side EF x = 7 x x Puzzles, Twisters & Teasers Down 8 16 = 7 x 1. FIGURES 2. SIMILAR 4. SEVEN 6. ADD 7. EVEN Across 3. SIDES 5. MEASUREMENT 8. ELEVEN 9. TRI Challenge. 1. h = 18 feet 2. h = 12 feet 3. h = 19 feet 4. h = 25 feet Problem Solving 1. 1,667 feet 2. 1,454 feet 3. 8 feet 11 inches feet 5. C 6. G 7. C 8. F S I M I L A R Reading Strategies 1. side DE 2. side DF
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