Pre-Calculus Homework Solutions 157

Pre-Calculus Homework Solutions 157 - 41. AG DC GF DC 14...

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41. AG 5 AD 2 GD 5 12 2 4.5 5 7.5 42. } D G C F } 5 ¬ } A A D G } } D 14 C } 5 ¬ } 7 1 . 2 5 } 7.5( DC ) 5 14(12) 7.5( DC ) 5 168 DC 5 ¬ 22.4 43. m / ADC 5 m / AGF 5 108 44. } B E C F } 5 ¬ } A A D G } } B 8 C } 5 ¬ } 7 1 . 2 5 } 7.5( BC ) 5 8(12) 7.5( BC ) 5 96 BC 5 ¬ 12.8 45. AB 1 BC 1 CD 1 AD 5 26 1 12.8 1 22.4 1 12 5 73.2 46. } A A E B } 5 ¬ } A A D G } } A 2 E 6 } 5 ¬ } 7 1 . 2 5 } 12( AE ) 5 ¬ 26(7.5) 12( AE ) 5 ¬ 195 AE 5 ¬ 16.25 AE 1 EF 1 FG 1 AG 5 16.25 1 8 1 14 1 7.5 5 45.75 47. } 4 7 5 3 .7 .2 5 } 5 } 8 5 } 48. n ABC , n IHG , n JLK and n NMO , n PRS ; / A > / I > / J because each one measures 53º. / B > / H > / L because each one is a right angle. / C > / G > / K because each one measures 90º-53º or 37º. So all corresponding angles are congruent. Now determine whether corresponding sides are proportional. Sides opposite 90º angle. } A IG C } 5 } 1 5 0 } 5 } 1 2 } } A JK C } 5 } 1. 5 25 } 5 4 } J IG K } 5 } 1 1 .2 0 5 } 5 8 Sides opposite 53º angle. } H BC G } 5 } 4 8 } 5 } 1 2 } } B LK C } 5 } 4 1 } 5 4 } H LK G } 5 } 8 1 } 5 8 Sides opposite 37º angle. } A IH B } 5 } 3 6 } 5 } 1 2 } } A JL B } 5 } 0. 3 75 } 5 4 } J IH L } 5 } 0. 6 75 } 5 8 The ratios of the measures of the corresponding sides are equal, and the corresponding angles are congruent, so n ABC , n IHG , n
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