Quadrilateral 81097

The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determine the length of segment EF.

Correct answer:

EF =  6.9282 cm

Step-by-step explanation:

AC=12 cm BC=6 cm AB=AC2BC2=12262=6 3 cm10.3923 cm AD=AB=10.3923=6 3 cm10.3923 cm  ACD=π180°arcsin(AB/AC)=π180°arcsin(10.3923/12)=60   EF=EC=CF FCE=60  FEC = EFC = FCE = 60    ECB=ACDFCE/2=6060/2=30   cos ECB = BC: CE  CE=BC/cosECB=BC/cos29.999999999997° =6/cos29.999999999997° =6/0.866025=6.9282 cm  EF=CE=6.9282=4 3=6.9282 cm

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