How to Calculate Magnitude and Direction for Orv's Walk?

[lalahelp]

Homework Statement

Orv walks 312 m due east. He then continues walking along a straight line, but in a different direction, and stops 220 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?
What is the magnitude?
What is the direction ___________ ° counterclockwise from the +x-axis

Homework Equations

C=squareroot of 312^2+220^2
What equation to use to find direction??

The Attempt at a Solution

C= Magnitude= 381.76 m why is my magnitude wrong?

 

[MSZShadow]

A good idea here is to read the problem carefully, and/or make a simple diagram.
You're correct in using the Pythagorean theorem for this problem, but you're using it incorrectly. Remember that the form is a^2 + b^2 = c^2, where c is the hypotenuse.

In the problem statement, you're given a = 312 meters (The distance walked east -- one of the legs of the triangle), and c = 220 meters (The distance in a straight line from the starting point -- the hypotenuse).

This means that what you need to find here is b, not c.

 

[Gordanier]

As with regards to your direction issues, once you have your three sides figured out, use your trig laws (soh cah toa).

If you've never heard of them, it goes:
"soh" - sin = opposite / hypotenuse
"cah" - cosine = adjacent / hypotenuse
"toa" - tangent = opposite / adjacent

And you should get the right answer.
Cheers

EDIT: or your sin/cosine laws. I didn't work through the problem myself, I just assumed based on the level it was a right angle triangle.

 

[MSZShadow]

EDIT: or your sin/cosine laws. I didn't work through the problem myself, I just assumed based on the level it was a right angle triangle.

Same. Now that I look at it (through my sleepy eyes), the 'hypotenuse' is shorter than one of the legs, and by a good bit, too...

 

[lalahelp]

I can't take the square root of a negative number for the magnitude... Is there another way to solve this...

 

[AC130Nav]

Homework Statement

Orv walks 312 m due east. He then continues walking along a straight line, but in a different direction, and stops 220 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?
What is the magnitude?
What is the direction ___________ ° counterclockwise from the +x-axis

Did you ever draw it?

 

[Quantum Mind]

@:AC130NAV: The problem states that the final position was 220 m from the starting point in an north easterly direction, so your drawing is not correct.