Angle Between

// If the player is within the circle and their bounding box's center is
// within 45 * 0.6 degrees from the line down the center of the opening,
// then they are safe.
const float InitialWheelRotation = 90.0f;
float wheelAngleDegrees = m_wheelEntity->getRotation() - InitialWheelRotation;
if (wheelAngleDegrees < -180.0f) wheelAngleDegrees += 360.0f;
float playerAngleDegrees = atan2(playerCenter.y - wheelCenter.y, playerCenter.x - wheelCenter.x) * 180.0f / AGLIB_PI - 90;

if (abs(wheelAngleDegrees - playerAngleDegrees) < 45.0f * 0.6f)
{
    // Safe in the gap!
    return false;
}