Trig question.. finding an exact expression.

A cruise ship sailed north for 50 km. Then, the captain turned the ship eastward through an angle of pi/6 and sailed an additional 50 km. Without using a calculator, determine an exact expression for the direct distance from the start to the finish of the cruise.

So I started by trying to draw the problem:

http://img402.imageshack.us/img402/2...ipquestion.png

Did I even draw it right? And to finish it off how do I determine an exact expression? Please show all work done to get to the expression.

**Answer: **

http://img529.imageshack.us/img529/3...shipanswer.png