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COURSE 3 LESSON 5-8 Similarity and Indirect Measurement When a 6-ft student casts a 17-ft shadow, a flagpole casts a shadow that is 51 ft long. Find the height of the flagpole. Set up a proportion for the similar triangles. Words flagpole’s height length of flagpole’s shadow = student’s height length of student’s shadow Let h = the flagpole’s height. Proportion 17h = 6 • 51 17h 6 • 51 = 17 17 h = 18 h 6 51 17 = Write the cross products. Divide each side by 17. Simplify. The height of the flagpole is 18 ft. 5-8 COURSE 3 LESSON 5-8 Similarity and Indirect Measurement In the figure below, ABC ~ EDC. Find d. Use similar triangles to set up a proportion involving the lengths of corresponding sides. ED CD = AB CB ED corresponds to AB. CD corresponds to CB. d 141 = 416 312 Substitute. 312 • d = 416 • 141 Write the cross products. 5-8 COURSE 3 LESSON 5-8 Similarity and Indirect Measurement (continued) 312d = 58,656 Simplify. 312d 58,656 = 312 312 Divide each side by 312. 58,656 312 Use a calculator. 188 The length of d is 188 m. 5-8 COURSE 3 LESSON 5-8 Similarity and Indirect Measurement 1. A 5-ft tall student casts a 12-ft shadow. A tree casts a 27-ft shadow. How tall is the tree? 11.25 ft tall 2. A 6-ft man casts a 9-ft shadow. A sculpture casts a 45-ft shadow. How tall is the sculpture? 30 ft 5-8