exploration Georgia Performance Standards M6G1.c, M6A2.c, M6A2.g Te eigts of very tall structures can be measured indirectly using similar figures and proportions. Tis metod is called indirect measurement. Augustine and Carmen want to measure te eigt of te scool s flagpole. To do tis, tey go outside and old a meterstick uprigt. Te meterstick casts a sadow tat measures 50 cm. 100 cm 50 cm 1. If te sadow of te flagpole measures 6 meters, ow tall is te flagpole? To answer tis question, follow tese steps: a. Draw a sketc of te flagpole and its sadow next to te sketc of te meterstick and its sadow. b. Label te eigt of te flagpole x. c. Write te proportion sadow of flagpole sadow of meterstick, and substitute te values for te given measurements. d. Solve te proportion for x. Tink and Discuss eigt of flagpole 2. Explain ow you solved te proportion for x in number 1d. 3. Explain weter you could ave solved te problem by sadow of flagpole sadow of meterstick writing te proportion as. eigt of flagpole eigt of meterstick eigt of meterstick 218 Holt Matematics
Tecnology Lab Use your computer tools to draw a diagram tat elps you model indirect measurement. Activity It s spirit week at scool and your team wants to decorate te ligt poles in te front of te building wit strings of pennants in your scool s colors. Te pennants are strung togeter and sold by te foot. To know ow many feet of pennants to buy, you need to know te eigt of te ligt poles. 1. Te student wo will be used for a comparison is 5 feet and 11 inces tall. Te sadow cast by te student is 15 feet long. Te sadow cast by te ligt pole is 88 feet long. You will use drawing tools to create and label a model of te student and a ligt pole. 2. To make te drawing tools easily accessible, click on te View menu and select te Toolbars option. From tere, be certain Drawing is selected. 3. Draw te vertical line for te ligt pole. To draw a straigt line, coose te Line command, click in your document and drag te line across te screen. Ten, draw te orizontal line for te sadow. Tis line sould start at te bottom of your first line. Ten make lines for te student and te student, s sadow. 4. Be sure to make your lines te rigt lengts. For example, te line for te student, s sadow sould be longer tan te line for te pole. Also, te line for te student sould be sorter tan te line for te pole. 5. To make tis drawing a useful problem-solving tool for mat, te illustration sould be labeled. Coose Text Box from te Insert menu. Type te label information into te box. Click and drag on te box andles to resize and reposition te words witin te illustration. 219 Holt Matematics
Tecnology Lab, continued 6. Find te ratio of eigt to sadow to determine te eigt of te ligt. Te ratios you constructed sould look like tis. Remember to cange all units to inces. 5fee t 11 inces feet 71 inces inces 15 feet 8 8 feet 1 80 inces 10 56 inces Tink and Discuss 1. Tere are six ligt poles in te front of scool. Will you be able to buy enoug flags for eac of te poles if tey cost $0.80 per foot and you ave $155.00 to spend on te project? Try Tis 1. Complete te following ratios to compute te eigt of te missing side of tese rigt triangles. 5 2 0 1 20 9 7 21 2. On a separate piece of paper, draw an illustration and sow te ratio for a redwood tree tat is 200 feet in eigt tat casts a sadow 500 feet long. 220 Holt Matematics
Review for Mastery If you cannot measure a lengt directly, you can use indirect measurement. Indirect measurement uses similar figures and proportions to find lengts. Te small tree is 8 feet ig and it casts a 12-foot sadow. Te large tree casts a 8 ft 36-foot sadow. Te triangles formed by te trees and te sadows are similar. So, teir eigts are proportional. To find te eigt of te large tree, first set up a proportion. Use a variable to stand for te eigt of te large tree. 8 1 2 3 x6 Write a proportion using corresponding sides. 8 36 12 x Te cross products are equal. 12x 288 x is multiplied by 12. 1 2x 2 88 Divide bot sides by 12. 12 12 x 24 So, te eigt of te tall tree is 24 feet. x 12 ft 36 ft Use indirect measurement to find te missing eigts. 1. 2. x 75 ft 6 ft 3 ft 15 ft 25 ft 10 ft 221 Holt Matematics
Homework and Practice Write te correct answer. 1. Use similar triangles to find te eigt of te building. 2. Use similar triangles to find te eigt of te tree. 6 ft 3 m 13 ft 39 ft 4 m 36 m 3. A lamppost casts a sadow tat is 15 yards long. A 3-foot-tall mailbox casts a sadow tat is 5 yards long. How tall is te lamppost? 4. An 8-foot-tall statue stands in te park and casts a sadow tat is 16 feet long. A dog stands next to it and is 3 feet tall. How long is te dog's sadow? 5. A building casts a sadow tat is 420 meters long. At te same time, a person wo is 2 meters tall casts a sadow tat is 24 meters long. How tall is te building? 6. On a sunny day around noon, a tree casts a sadow tat is 12 feet long. At te same time, a person wo is 6 feet tall standing beside te tree casts a sadow tat is 2 feet long. How tall is te tree? 7. A pole casts a sadow tat is 21 feet long. A 3-feet-tall cild standing next to te pole casts a sadow tat is 9 feet long. How tall is te pole? 8. Jeremy as two tropies next to eac oter sitting in te window of is room. His football tropy is 7 inces tall and is basketball tropy is 13 inces tall. As te ligt sines in, te basketball tropy s sadow measures 26 inces. How long is te football tropy s sadow? 222 Holt Matematics