38. Given:nABCwithsides of measure a,b, and c,where c25a21b2Prove:nABCis aright triangle.Proof:Draw DE##on line ,with measure equal toa.At D,draw line m ' DE##.Locate point Fon mso that DF5b.Draw FwEwand call its measure x.Because nFEDis a right triangle,a21b25x2.But a21b25c2, so x25c2or x5c.Thus,nABC>nFEDby SSS. This means /C>/DE.Therefore,/Cmust be a right angle, makingnABCa right triangle.39. Given:nABCwith right angle at C,AB5dProve:d5Ï(x22wx1)21w(y22wy1)2wProof:40.First, use the Pythagorean Theorem to find thelength of the ladder, represented by y.12211625¬y214412565¬y24005¬y2Ï400w5¬y205¬yThe ladder is 20 feet long.(2112)21x25¬2021421x25¬2021961x25¬400x25¬204x5¬Ï204wx5¬2Ï51wx<¬14.3The ladder reaches about 14.3 feet up the side ofthe house.41.Let xbe the hypotenuse of the triangle withheight 26112 or 38 and base }12}(9) or 4.5.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.