A spinner used in a board game is divided into 9 equally sized sectors. Four of these sectors indicate that the player should move his token forward on the board, two of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board.
The total area of the sectors that do not allow the player to move his token is 14.6 inches squared.
What is the radius of the spinner?
your answer, rounded to the nearest tenth of an inch =
3 of the sectors are the ones that do not let the player move
So......these 3 sectors occupy a total central angle of (3/9) * 360 = 360/3 = 120°
So we can solve this
Area = (1/2) radius^2 sin (120°)
14.6 = (1/2) radius^2 * √3 / 2
14.6 = (√3 /4) * radius^2 multiply both sides by 4/√3
14.6 * (4/√3) = radius^2 take the positive square root of both sides
5.8 in = radius