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The problem you've shared involves a military plane flying at an altitude of 304.8 km, observing a submarine and a tank at depression angles of 37° and 21°, respectively. We are asked to calculate the horizontal distance between the submarine and the tank.

### Steps to solve:

1. **Understand the situation**:
   - The plane's altitude is the vertical height from which both the submarine and the tank are being observed.
   - The depression angles for the submarine and tank (37° and 21°) give us the direction in which the objects are located from the plane.
   
2. **Identify distances**:
   Using trigonometry, we can find the horizontal distance between the plane and the submarine and between the plane and the tank.

   For each object, we can use the formula for horizontal distance:
   \[
   \text{Distance to object} = \frac{\text{Altitude}}{\tan(\text{Depression angle})}
   \]

   Let's denote:
   - \( h = 304.8 \) km (altitude of the plane)
   - \( \theta_1 = 37^\circ \) (depression angle to the submarine)
   - \( \theta_2 = 21^\circ \) (depression angle to the tank)

   Therefore, the horizontal distances to the submarine (\(d_s\)) and the tank (\(d_t\)) are:
   \[
   d_s = \frac{h}{\tan(\theta_1)} = \frac{304.8}{\tan(37^\circ)}
   \]
   \[
   d_t = \frac{h}{\tan(\theta_2)} = \frac{304.8}{\tan(21^\circ)}
   \]

3. **Find the distance between the submarine and the tank**:
   The total distance between the submarine and the tank will be the difference in their horizontal distances from the plane:
   \[
   \text{Distance between submarine and tank} = |d_s - d_t|
   \]

Let's calculate this now.The horizontal distances are:

- Distance from the plane to the submarine: \( 404.48 \, \text{km} \)
- Distance from the plane to the tank: \( 794.03 \, \text{km} \)

Thus, the distance between the submarine and the tank is approximately \( 389.55 \, \text{km} \).

Would you like more details or have any questions?

### Related questions:
1. How does the angle of depression affect the horizontal distance?
2. How would the solution change if the plane's altitude were doubled?
3. What if the angles of depression were swapped between the tank and the submarine?
4. How can we apply this concept to real-life navigation and targeting?
5. How would the result change if the angle of depression for the submarine was increased by 10°?

### Tip:
In trigonometry problems involving angles of depression, always ensure that the vertical and horizontal components are correctly identified, especially in practical applications like aviation and navigation.

Un avión militar vuela a una altura de 304.8 Km, localiza un submarino a un ángulo de depresión de 37° y un tanque a un ángulo de depresión de 21°. Calcular la distancia entre el tanque y el submarino.

Calculate the distance between a submarine and a tank from a military plane at an altitude of 304.8 km, with depression angles of 37° and 21°, using trigonometric methods. Suitable for Grades 10-12 students studying trigonometry.

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