Two ships leave a port at the same instant. One sails at 30km/hr in the direction N 32° E while the other sails at 20 km/hr in the direction S 58° E. After two hours the ships are distant from each other by.

Let us draw a figure below as per given question.
Let two ships started from point O at the speed of 30 km/hr and 20 km/hr respectively, after two hours they reach at points A and B.
Now, ∠NOA = 32° and ∠SOB = 58° ,
Then, ∠AOB = 180° - (32° + 58°) = 90°
Since ΔAOB is a right triangle in which OA = 2 x 30 = 60 km and OB = 2 x 20 = 40 km
Since, AB = √OA² + OB²
= √(60)² + (40)²
= √5200
= 20√13