# Trig question.. finding an exact expression.

• Dec 2nd 2009, 04:02 PM
kmjt
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.

• Dec 2nd 2009, 07:21 PM
Quote:

Originally Posted by kmjt
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.

HI

you can use the cosine rule ,

$\displaystyle x^2=50^2+50^2-2(50)(50)\cos 30$
• Dec 5th 2009, 12:20 PM
kmjt
So I did the cosine rule as you mentioned:

a^2 = b^2 + c^2 -2bc(cos30)

a^2 = 50^2 + 50^2 - 2(50)(50)cos30

a^2 = 2500 + 2500 - 5000 (0.866)

a^2 = 2500 + 2500 - 4330.127

a^2 = 669.873

a = 25.88190488

I'm confused as to how doing that would help me determine an exact expression for the direct distance from the start to the finish of the cruise. I have no clue where the expression is coming from, please help. Once again the expression for the direct distance from the start to finish of the cruise is: