An airplane is 149 miles north and 90 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should the pilot take? (Enter your answer clockwise from north. Round your answer to one decimal place.)
31
 
Incorrect: Your answer is incorrect.
 ° clockwise from north

To solve this problem, we need to determine the angle (bearing) that the pilot should fly to reach the airport from the plane’s current position. We can approach this by using trigonometry, specifically the tangent function.

### Step-by-step solution:

1. **Positioning the airplane**:
   - The airplane is 149 miles north and 90 miles east of the airport.
   - We need to find the angle from the north direction (clockwise) that will take the plane directly to the airport.

2. **Determine the angle**:
   Since the airplane's position can be seen as a right triangle where:
   - The vertical leg (opposite) is the distance north, 149 miles.
   - The horizontal leg (adjacent) is the distance east, 90 miles.
   
   To find the angle relative to the north, we calculate the angle between the eastward direction and the line from the airplane to the airport.

3. **Using the tangent function**:
   The angle \(\theta\) relative to east can be found using the tangent formula:
   \[
   \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{90}{149}
   \]
   \[
   \theta = \tan^{-1}\left(\frac{90}{149}\right)
   \]
   Using a calculator:
   \[
   \theta = \tan^{-1}(0.604) \approx 31.0^\circ
   \]

4. **Final bearing**:
   The bearing is measured clockwise from the north. Since this angle is measured clockwise from the east (90 degrees), the final bearing is:
   \[
   \text{Bearing} = 90^\circ - 31.0^\circ = 59.0^\circ
   \]

### Answer:
The bearing the pilot should take is **59.0° clockwise from north**.

Would you like more details on any part of the solution or have any questions? Here are some related questions you might find useful:

1. How do we use the tangent function to find angles in navigation?
2. Why do we subtract the angle from 90° to get the final bearing?
3. What would be the bearing if the distances north and east were swapped?
4. How does the Pythagorean theorem relate to finding bearings in this context?
5. What tools can pilots use to calculate bearings accurately?

**Tip**: Always visualize the position as a right triangle when calculating angles in navigation problems like this one!

An airplane is 149 miles north and 90 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should the pilot take? (Enter your answer clockwise from north. Round your answer to one decimal place.)

Learn how to calculate the bearing an airplane should take to fly directly to an airport using trigonometry. This detailed solution covers the use of the tangent function to find angles in a right triangle. The airplane is 149 miles north and 90 miles east of the airport, and the solution shows how to determine the correct bearing.

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