find your distance from the starting point in m. That is, you first walk leg B, which is 24 m in a direction exactly 44° west of north, and then leg A, which is 11.5 in a direction exactly 15° south of west.

To find the distance from the starting point after walking the two legs of the journey, we can use vector addition and trigonometry. We treat each leg of the journey as a vector, resolve them into their components, and then sum those components to get the resultant displacement vector.

### Step 1: Break down each vector into its components

#### Vector B (24 m at 44° west of north)
This vector is directed 44° west of north, so the angle relative to the positive \(y\)-axis (north) is 44°.

- The north (or y) component:  
  \( B_y = 24 \times \cos(44^\circ) \)
  
- The west (or x) component:  
  \( B_x = -24 \times \sin(44^\circ) \)  
  (negative because it’s westward)

#### Vector A (11.5 m at 15° south of west)
This vector is directed 15° south of west, so the angle relative to the negative \(x\)-axis (west) is 15°.

- The west (or x) component:  
  \( A_x = -11.5 \times \cos(15^\circ) \)

- The south (or y) component:  
  \( A_y = -11.5 \times \sin(15^\circ) \)  
  (negative because it’s southward)

### Step 2: Sum the components

Now sum the x-components and y-components of vectors A and B to get the total displacement components.

- Total x-component:  
  \( x_{\text{total}} = B_x + A_x \)

- Total y-component:  
  \( y_{\text{total}} = B_y + A_y \)

### Step 3: Find the magnitude of the resultant displacement

The distance from the starting point is the magnitude of the resultant vector, which is given by:

\[
d = \sqrt{(x_{\text{total}})^2 + (y_{\text{total}})^2}
\]

Let me calculate this.The distance from the starting point is approximately 31.24 meters.

Would you like a detailed breakdown of the steps or any further clarifications?

Here are 5 related questions to expand your understanding:
1. How can vector addition be used in other real-life navigation problems?
2. What is the significance of resolving vectors into components?
3. How would the process change if you had three or more legs in the journey?
4. What is the difference between displacement and distance traveled?
5. How would the result change if you changed the direction of the legs?

**Tip:** Always check the direction of each vector component carefully, as positive and negative signs are crucial in vector addition.

Find the distance from the starting point after walking two legs of a journey: 24 meters west of north and 11.5 meters south of west. This solution uses vector addition, trigonometry, and the Pythagorean theorem to compute the resultant displacement. Suitable for students in Grades 10-12.

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