# Thread: Trig question.. finding an exact expression.

1. ## 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:

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:

2. 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:

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:
HI

you can use the cosine rule ,

$\displaystyle x^2=50^2+50^2-2(50)(50)\cos 30$

3. 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:

I have no clue where thats coming from

4. I'm also quite confused about the wording of the question and what the diagram should look like. P.S. When you used the cosine law it is not same as the rounded answer from the back of the text. The rounded answer should be approx 96.93 not 25.88. Also my class has not been taught to use the cosine law yet so I'm pretty sure you're not supposed to use it. If you are using Advanced Functions 12 by McGraw-Hill Ryerson.

5. This is basically what my diagram looked like. I do believe I was able to get the right answer. Sorry about the bad diagram.

6. Yup your diagram is exactly correct. I figured it it yesterday and I also got 96.93