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To determine the airplane's actual bearing in this problem, we need to account for the effect of the wind on the airplane's intended course. This problem involves vector addition since the airplane's airspeed and the wind are acting in different directions.

### Problem Summary
- **Airplane's airspeed** (relative to the air): \( 145 \, \text{km/h} \)
- **Desired course** (direction the airplane wants to maintain): \( 67^\circ \)
- **Wind speed**: \( 26 \, \text{km/h} \)
- **Wind direction**: \( 337^\circ \) (measured clockwise from north)

Our goal is to find the **actual bearing** the airplane should take to maintain a track of \( 67^\circ \).

### Solution Steps
1. **Convert Directions to Vector Components**:
   - For each vector (the airplane’s intended course and the wind), we need to find the north and east components using trigonometry.

2. **Breakdown of Vectors**:
   - **Airplane's Velocity Vector** (145 km/h at 67°):
     - \( V_{\text{plane, east}} = 145 \cos(67^\circ) \)
     - \( V_{\text{plane, north}} = 145 \sin(67^\circ) \)
   - **Wind Velocity Vector** (26 km/h at 337°):
     - \( V_{\text{wind, east}} = 26 \cos(337^\circ) \)
     - \( V_{\text{wind, north}} = 26 \sin(337^\circ) \)

3. **Calculate Components**:
   Substitute these values and calculate the components.

4. **Determine Required Heading**:
   To counter the wind and maintain a track of 67°, the airplane's resultant velocity (sum of its own velocity and the wind velocity) should have a bearing of 67°.

5. **Compute Actual Bearing**:
   Using trigonometry, adjust the airplane's direction to find the required initial bearing that will result in the desired track after adding the wind effect.

I'll calculate these values to determine the final bearing.The airplane's actual bearing should be approximately **56.8°** to maintain its intended course of 67° after accounting for the wind's effect. This result is rounded to the nearest tenth as required.

Would you like further details or have any questions on the process?

Here are some related questions for further exploration:
1. How would the answer change if the wind speed were higher?
2. What if the airplane's desired course was different, say 90°?
3. How can vector addition be visualized in this scenario?
4. How does wind direction impact the airplane's ground speed?
5. Why is it necessary to adjust the airplane's heading in the presence of wind?

**Tip:** In aviation navigation, calculating headings with wind adjustments is often done using an E6B flight computer, a tool designed to simplify these vector-based calculations.

An airplane has an airspeed of 145 km/h. The direction of its track, or course, is 67° while a 26-km/h wind is blowing from 337°. What must the airplane's actual bearing be to maintain this current track?

Learn how to calculate an airplane's required bearing to maintain a specified track direction of 67° when facing a 26 km/h wind blowing from 337°. This problem involves trigonometric vector components and adjustments for wind correction, suitable for Grades 11-12.

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