To find the bearing of C from A, we need to determine the angle $\theta$ that the line $AC$ makes with the due north direction.

Step 1: Identify Key Information

• $AB = 360$ km
• $BC = 100$ km
• $AC = 374$ km

We have a right-angled triangle $\triangle ABC$, where:

• $AB$ is the northward leg.
• $BC$ is the eastward leg.
• $AC$ is the hypotenuse.

Step 2: Find the Bearing Angle $\theta$

The bearing of C from A is measured clockwise from north to the line $AC$. This means we need to find the angle $\theta$ where:

$\theta = \tan^{-1} \left( \frac{BC}{AB} \right)$

Substituting values:

$\theta = \tan^{-1} \left( \frac{100}{360} \right)$

$\theta = \tan^{-1} (0.2778)$

$\theta \approx 15.4^\circ$

Step 3: Final Bearing

Bearings are measured clockwise from north, so the bearing of C from A is:

$\mathbf{015.4^\circ}$

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Do you want further clarification or step-by-step breakdown?

Here are five related questions for practice:

1. What would be the bearing if the aircraft had traveled west instead of east?
2. How would the bearing change if $BC$ was longer?
3. How can the Pythagorean theorem verify the distance $AC$?
4. How would you determine the total displacement of the aircraft?
5. What is the aircraft's average velocity during the journey?

Tip:

Bearings are always given in three-digit notation, so if the calculated angle is less than 100°, add a leading zero (e.g., $015^\circ$ instead of $15^\circ$).