Pre-Calculus Homework Solutions 196

Pre-Calculus Homework Solutions 196 - m 38. Given: ABC with...

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38. Given: n ABC with sides of measure a , b , and c ,where c 2 5 a 2 1 b 2 Prove: n ABC is a right triangle. Proof: Draw DE ## on line , with measure equal to a .At D ,draw line m ' DE ## .Locate point F on m so that DF 5 b .Draw F w E w and call its measure x . Because n FED is a right triangle, a 2 1 b 2 5 x 2 . But a 2 1 b 2 5 c 2 , so x 2 5 c 2 or x 5 c .Thus, n ABC > n FED by SSS. This means / C > / DE . Therefore, / C must be a right angle, making n ABC a right triangle. 39. Given: n ABC with right angle at C , AB 5 d Prove: d 5 Ï ( x 2 2 w x 1 ) 2 1 w ( y 2 2 w y 1 ) 2 w Proof: 40. First, use the Pythagorean Theorem to find the length of the ladder, represented by y . 12 2 1 16 2 5 ¬ y 2 144 1 256 5 ¬ y 2 400 5 ¬ y 2 Ï 400 w 5 ¬ y 20 5 ¬ y The ladder is 20 feet long. (2 1 12) 2 1 x 2 5 ¬ 20 2 14 2 1 x 2 5 ¬ 20 2 196 1 x 2 5 ¬ 400 x 2 5 ¬ 204 x 5 ¬ Ï 204 w x 5 ¬ 2 Ï 51 w x < ¬ 14.3 The ladder reaches about 14.3 feet up the side of the house. 41. Let x be the hypotenuse of the triangle with height 26 1 12 or 38 and base } 1 2 } (9) or 4.5.
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