1. ## Word problem confusion

The question:

A cruise ship sailed north for 50km. Than the captain turned the ship eastward through an angle of pi/6 and sailed an additional 50km. Without using a calculator, determine an exact expression for the direct distance from the start to the finish of the cruise.
Answer at the back of the book: sqr(5000+2500sqr3) km

Seems pretty simple and maybe I'm thinking of this question the wrong way, but I can't seem to figure out where they got that answer.

All help greatly appreciated!

2. Draw the "triangle"...

3. Originally Posted by Also sprach Zarathustra
Draw the "triangle"...
I've tried...but wasn't very successful I got a different answer that what it states in the back of the book so I was wondering if either I did something wrong or if the book made a mistake.

4. Recall the special triangles you learned in class. Do you remember this one? You've probably seen this in the form of radian angles and with sides 1, 2, sqrt(3). (pi/6 = 30 degrees)

Use this ratio to determine the total displacement north and displacement east. then use Pythagoras to find x.