## Task 3 - 320623

A scout group receives the following instructions for a field game:

- Start from point $A$ and walk $600 \mathrm{~m}$ straight north! There you will find an observation tower (point B).
- Now change your course by $60^{\circ}$ in a northeasterly direction! After $500 \mathrm{~m}$ you will reach an old barn (point $C$).
- Now walk $700 \mathrm{~m}$ at a right angle in a roughly southeasterly direction! There you will find a hollow oak tree (point $D$). From there, you need to find your way back to $A$.

a) By how many degrees must the scout group change their course in $D$ to head straight back to $A$?

b) How long is the distance from $A$ to $D$?

c) A member of the group wants to return to $A$ from $C$. How far is $A$ from $C$?

To answer these questions, make a drawing (on white, not graphed or lined paper; in an appropriate scale); use the drawing to determine the required information with the precision of the drawing!
The figure shows a representation where $100 \mathrm{~m}$ is scaled down to $1 \mathrm{~cm}$. From such a drawing, one can read with drawing accuracy (approximately $1^{\circ}$ precise or about $1 \mathrm{~mm}$ precise, i.e., for distances about $10 \mathrm{~m}$ precise):

a) In $D$, the course must be changed by $\delta \approx 103^{\circ}$ (approximately in a southwesterly direction).

b) The distance from $D$ to $A$ is approximately $820 \mathrm{~m}$.

c) Point $A$ is about $950 \mathrm{~m}$ away from $C$.

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0283.jpg?height=580&width=577&top_left_y=932&top_left_x=748)