Thread: 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!

Draw the "triangle"...

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.

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.