As observed from the top of a \(64 \ m\) high lighthouse from the sea level, the angles of depression of two ships are \(28^{\circ}\) and \(45^{\circ}\). If one ship is exactly behind the other on the same side of the lighthouse, calculate the distance between the two ships. (\(tan \ 28^{\circ} = 0.5317\))
Solution:
Let \(CD\) be the height of the lighthouse and \(D\) is the position of the observer.
Let \(A\) and \(B\) be the position of two ships.
In the right \(\triangle DCB\), \(= \frac{CD}{CB}\)
In the right \(\triangle DCA\), \(= \frac{CD}{CA}\)
Therefore, the distance between the two ships \(=\) .
(Note: Enter the number rounded to two decimal places in the first box and the unit (short form) in the second box.)