Pre-Calculus Homework Solutions 161

Pre-Calculus Homework Solutions 161 - 19 DC EB so ADC AEB...

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19. D w C w ± E w B w , so / ADC > / AEB and / ACD > / ABE because they are corresponding angles. By AA Similarity, n ABE , n ACD . } A A B C } 5 ¬ } A A D E } } x 1 x 1 2 1 2 6 } 5 ¬ } 8 2 8 5 } 8( x 1 2) 5 ¬ ( x 1 8)(3) 8 x 1 16 5 ¬ 3 x 1 24 5 x 1 16 5 ¬ 24 5 x 5 ¬ 8 x 5 ¬ } 8 5 } AB 5 x 1 2 5 } 8 5 } 1 2 or 3 } 3 5 } AC 5 x 1 2 1 6 5 } 8 5 } 1 2 1 6 or 9 } 3 5 } 20. n ABD and n FEC are right triangles with / A > / F and right angles B and E .Because all right angles are congruent, n ABD , n FEC by AA Similarity. } B C D E } 5 ¬ } A FE B } } x x 2 1 1 2 } 5 ¬ } 3 8 } 8( x 2 1) 5 ¬ 3( x 1 2) 8 x 2 8 5 ¬ 3 x 1 6 5 x 2 8 5 ¬ 6 5 x 5 ¬ 14 x 5 ¬ } 1 5 4 } BD 5 ¬ x 2 1 5 ¬ } 1 5 4 } 2 1 or } 9 5 } EC 5 ¬ x 1 2 5 ¬ } 1 5 4 } 1 2 or } 2 5 4 } 21. n ABC and n ARS are right triangles with / A > / A and right angles / ASR and / ACB . Because all right angles are congruent, n ABC , n ARS by AA Similarity. } A A C S } 5 ¬ } C SR B } } 1 x 2 } 5 ¬ } 6 9 } 9 x 5 ¬ 72 x 5 ¬ 8 AB 5 ¬ x 1 7 5 ¬ 8 1 7 or 15 AS 5 ¬ x 5 ¬ 8 22. AB 5 Ï 6 2 1 1 w 2 2 w 5 Ï 180 w or 6 Ï 5 w BC 5 Ï 6 2 1 3 w 2 w 5 Ï 45 w or 3 Ï 5 w CA 5 |7 2 ( 2 8)| 5 15 ST
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