Question

"Rebecca walks 100 feet in a straight line. She then turns 20 degrees to her left and walks another 100 feet, and then turns 20 degrees to her left again. She continues this pattern until she reaches the point where she started. How far did she walk

Answer 1

1,800 ft

Explanation:

Rebecca will walk in the pattern of a regular polygon with 'n' sides and internal angles of 160 degrees (180 at a straight line - 20 degrees from each turn).

The equation that describes the internal angle of a regular polygon is:

`A = ((n-2)*180)/(n)`

For A = 160 degrees:

`160n=(n-2)*180\\(180-160)n=360\\n=18\ sides`

If each side is 100 ft long, the total distance that Rebecca has walked is:

`d = 18*100\\d=1,800\ ft`

She walked 1,800 ft.