The angle of elevation of the top of a 75 m lower from a ship and a boat are 26.4 and 57.4 respectively. Given that, the ship, boat and the foot of the tower are on the same horizontal.

Let $H$ be the height of the tower, $H = 75$ m.
Let $d_S$ be the distance from the foot of the tower to the ship.
Let $d_B$ be the distance from the foot of the tower to the boat.
The angle of elevation from the ship is $\theta_S = 26.4^\circ$.
The angle of elevation from the boat is $\theta_B = 57.4^\circ$.
Using the tangent function for right-angled triangles ($\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$):

$$d_S = \frac{H}{\tan(\theta_S)}$$ $$d_B = \frac{H}{\tan(\theta_B)}$$

The distance between the ship and the boat is $D = d_S - d_B$.

Substitute the values into the formula for $d_S$:

$$d_S = \frac{75}{\tan(26.4^\circ)}$$ $$d_S \approx \frac{75}{0.495726}$$ $$d_S \approx 151.299 \text{ m}$$

Substitute the values into the formula for $d_B$:

$$d_B = \frac{75}{\tan(57.4^\circ)}$$ $$d_B \approx \frac{75}{1.562309}$$ $$d_B \approx 48.006 \text{ m}$$

Subtract $d_B$ from $d_S$:

$$D = d_S - d_B$$ $$D = 151.299 \text{ m} - 48.006 \text{ m}$$ $$D = 103.293 \text{ m}$$

The distance between the ship and the boat, corrected to three significant figures, is:

$$103 \text{ m}$$