Calculating Anna's Final Position

The problem asks for the distance and direction Anna is from her starting point after a series of movements. This is a displacement problem.

Analyzing Anna's Movements

• Initial Movement: Anna walks 15 meters south.
• Second Movement: She turns right. Since she was walking south, turning right means she now walks west. She walks 20 meters west.

These movements can be visualized as two perpendicular legs of a right-angled triangle, where the starting point is one vertex, the point after walking south is another, and the final point is the third vertex.

Finding the Distance from the Starting Point

The distance from the starting point is the hypotenuse of the right-angled triangle formed by her path. We can use the Pythagorean theorem:

Distance$^2$ = (Southward distance)$^2$ + (Westward distance)$^2$

Let $d$ be the distance from the starting point.

$ d^2 = (15 \text{ m})^2 + (20 \text{ m})^2 $

$ d^2 = 225 \text{ m}^2 + 400 \text{ m}^2 $

$ d^2 = 625 \text{ m}^2 $

$ d = \sqrt{625 \text{ m}^2} $

$ d = 25 \text{ m} $

Determining the Direction

Anna moved 15 meters south and 20 meters west. Therefore, her final position relative to the starting point is in the south-west direction.

Final Displacement

Combining the distance and direction, Anna is 25 meters south-west from her starting point.