If an ant moves a distance x,then turn left 120 degree and travel x distance again and turn right 120 dgree and travel, he is 9 inches from the starting point, what is the value of x?
Pick one.
A) 9√9 B) 9√3 C) 9√6 D) 7√3 E) 9√4
See the above diagram. (A bit confusing though!!)   The ant starts from A travelled to B, turned 120 degrees left and travelled to C. and turned 120 degrees right and travelled to D.   From the diagram, ∠ACB=600∠ACB=600. As BC and AB are equal, ∠BCA=∠BAC=600∠BCA=∠BAC=600.   So ΔABCΔABC is equilateral.   Also ∠BCD=600∠BCD=600.   As, ∠ACB=∠BCD∠ACB=∠BCD equal, CB divides AD into two equal parts. Aso DE = 9/2.   In the triangle CED, Sin600=3–√2=92xSin600=32=92x   So x=9√3   Answer:9√3
<result>B</result>
If an ant moves a distance x,then turn left 120 degree and travel x distance again and turn right 120 dgree and travel, he is 9 inches from the starting point, what is the value of x?