From a lighthouse $75 \mathrm{~m}$ high, a ship is observed to be $1.3 \mathrm{~km}$ out at sea. What is the angle of depression of the ship from the lighthouse? Draw a neat diagram to start with to illustrate the situation.

Step 1 ：First, let us draw a diagram (not to scale!): [asy] pair A,B,C; A=(0,0); B=(0,75); C=(1300,0); draw(A--B--C--cycle); label("A",A,SW); label("B",B,NW); label("C",C,SE); [/asy]

Step 2 ：Here, $AB$ is the height of the lighthouse, $BC$ is the distance of the ship from the base of the lighthouse, and $AC$ is the distance between the ship and the lighthouse. We are given that $AB = 75\text{m}$ and $BC = 1.3\text{km} = 1300\text{m}$. We want to find the angle of depression $\angle BAC$.

Step 3 ：Since $\triangle ABC$ is a right triangle with $\angle ABC = 90^\circ$, we can use the tangent function to find the angle of depression. We have $\tan(\angle BAC) = \frac{AB}{BC} = \frac{75\text{m}}{1300\text{m}}$.

Step 4 ：Now, we can find the angle $\angle BAC$ by taking the inverse tangent of the ratio: $\angle BAC = \tan^{-1}\left(\frac{75}{1300}\right)$.

Step 5 ：Using a calculator, we find that $\angle BAC \approx 3.31^\circ$.

Step 6 ：\(\boxed{3.31}\) degrees is the angle of depression of the ship from the lighthouse.