<image> As shown in the figure, a ship departs from point \( A \) at sea level and heads \( 40^{\circ} \) south of west for \( 40 \) nautical miles to reach point \( B \). Then from point \( B \), it heads \( 20^{\circ} \) north of west for \( 40 \) nautical miles to reach point \( C \). The distance between points \( A \) and \( C \) is ______ nautical miles.