Is my answer correct? - related rates problem

[blueroses12]

Boat A is traveling away from the port in the direction 30degrees North of East (30 degrees above the positive x-axis) at a rate of 15 miles per hour. Boat B travels North and towards the port at a rate of 10 miles per hour. Find the rate of change of the distance between the two boats when Boat A is 45 miles from the port and Boat B is 30 miles from the port. Round your answer to two decimal places and make sure to include units.

Can someone check my work? I used the law of cosine to find the missing side. And then plugged everything in to find the rate of change of the distance between the two points. Also, I used negative 10mph for dB/dt since the distance of boat B is decreasing as its approaching the port.
Please let me know if I made a mistake somewhere. Thank you!

 

[Dr.Peterson]

This is a little better than the first thread that I just answered. You need to do what I suggested there.

In particular, you implicitly assumed that a^2 + b^2 = c^2, which is the "fact" you differentiated. Use the law of cosines, which you clearly know applies ...

 

[blueroses12]

This is a little better than the first thread that I just answered. You need to do what I suggested there.

In particular, you implicitly assumed that a^2 + b^2 = c^2, which is the "fact" you differentiated. Use the law of cosines, which you clearly know applies ...

So I used the law of cosines and differentiated it with respect to time. However, I still get the same answer as I did above.
Is this still wrong?
Here is my work:

 

[Dr.Peterson]

I didn't even check your answer before, since the work was clearly wrong! But as you can see by looking at your work this time, it just happens that the term you had omitted is zero and doesn't affect the answer.

(That's not a good way to design a problem, since you could accidentally get the right answer, and grading would require looking carefully at the steps!)

 

[blueroses12]

I didn't even check your answer before, since the work was clearly wrong! But as you can see by looking at your work this time, it just happens that the term you had omitted is zero and doesn't affect the answer.

(That's not a good way to design a problem, since you could accidentally get the right answer, and grading would require looking carefully at the steps!)

Sorry, I'm still confused on how to correctly set up the problem. I used the law of cosines and differentiated it, then plugged in all the numbers. I thought I was suppose to omit the zero?
I'm still quite confused

 

[Dr.Peterson]

Sorry, I'm still confused on how to correctly set up the problem. I used the law of cosines and differentiated it, then plugged in all the numbers. I thought I was suppose to omit the zero?
I'm still quite confused

My point was, your answer was correct both times, and your work was correct when you used the law of cosines (post #3).

It's just that if the numbers had been different in the problem, you would not get the 0 in the last term of the numerator, and the problem would be more interesting. That's the problem's fault, not anything you did wrong.