Answer :
To find the distance between the two ships, we can use trigonometry. Let's denote the distance between the plane and the first ship as \( x \) and the distance between the plane and the second ship as \( y \).
1. First, we need to create right triangles for each ship. The angles of depression give us the angles in these triangles, with the horizontal distance being the base and the vertical distance being the height of the triangle.
2. For the ship with a 35° angle of depression, we have:
\[ \tan(35^\circ) = \frac{265}{x} \]
Solving for \( x \), we get:
\[ x = \frac{265}{\tan(35^\circ)} \]
3. Similarly, for the ship with a 25° angle of depression, we have:
\[ \tan(25^\circ) = \frac{265}{y} \]
Solving for \( y \), we get:
\[ y = \frac{265}{\tan(25^\circ)} \]
4. The total distance between the two ships is the sum of \( x \) and \( y \). Therefore, the distance apart between the ships is:
\[ \text{Distance} = x + y = \frac{265}{\tan(35^\circ)} + \frac{265}{\tan(25^\circ)} \]
5. By substituting the values of \( \tan(35^\circ) \) and \( \tan(25^\circ) \), you can calculate the exact distance between the two ships.
This method utilizes trigonometry to determine the distance between the ships accurately.
