# Thread: Another oldie

1. ## Another oldie

A surveyor starts at the center of a circular park with radius 7 miles.

He walks 3 miles directly east and drives a stake into the ground at point $\displaystyle A.$

He walk directly north until he reaches the perimeter of the park.
Then he walks directly west until he is directly north of the center,
. . and drives a stake into the ground at point $\displaystyle B.$

Find the distance $\displaystyle \overline{AB}.$

[The shortest solution, please.]
.

2. here's the hint:

diagonals of a rectangle are ... ?

3. Originally Posted by Soroban
A surveyor starts at the center of a circular park with radius 7 miles.

He walks 3 miles directly east and drives a stake into the ground at point $\displaystyle A.$

He walk directly north until he reaches the perimeter of the park.
Then he walks directly west until he is directly north of the center,
. . and drives a stake into the ground at point $\displaystyle B.$

Find the distance $\displaystyle \overline{AB}.$

[The shortest solution, please.]
.
You have a rectangle one diagonal of which is a radius, AB is the other diagonal.

CB

4. Use pythagoras theorem, the shortest possible method, no need of trigonometry

CLUE: IT IS A SURD!!!!

5. Originally Posted by ice_syncer
Use pythagoras theorem, the shortest possible method, no need of trigonometry

CLUE: IT IS A SURD!!!!
don't think so ...

6. Originally Posted by skeeter
don't think so ...
no, use pythagoras theorem.

7. let me guess! 7 miles may be?

8. ^^The diagonals of a rectangle are equal, so it equals the radius, 7 miles.

9. I know this is a while afterwards but, the solution is quite simple.

One diagonal is a radius, so the Northern leg of the trip must be:

$\displaystyle 3^2 + b^2 = 7^2$

$\displaystyle b = \sqrt{40}$

So, the parallel side is also $\displaystyle \sqrt{40}$, so therefore the diagonal AB must be:

$\displaystyle 3^2 + (\sqrt{40})^2 = c^2$

$\displaystyle 7 = c$

And there you go.

10. You don't need to do that calculation. The two diagonals of a rectangle are of the same length and one of them is a radius. Since the circle is given as having radius 7 mi., the length of AB is 7 mi.