# How to find angle after applying Pythagorean Theorem?

Tags:
1. Oct 15, 2014

### LeighV

Hello, so I have a question that states (these aren't the actual measurements but they are around about the same, I can't remember the exact numbers so I made these up, this way I could apply the same to the actual numbers) an object being 4km above me, 1.4km to the north of me, and 2km to the west of another person. (I know the coordinates north, west, etc. are correct, just made a guess on the numbers) I have to find the angle to the object.

So i began for the xyz to begin applying the Pythagorean theorem, so
√4^2 + 1.4^2 + 2^2
16 + 1.96 + 4
4.69

But I am not sure where to go from here. I am guessing it would be either cos or sin I use?

Thank you for the guidance!

2. Oct 15, 2014

### Staff: Mentor

Draw a picture and mark your angle then it should be obvious which trig function to use.

Since you know all three sides, you get to choose your favorite one.

3. Oct 15, 2014

### SteamKing

Staff Emeritus
Since you apparently are dealing with a 3-D problem, you'll need more than one angle to determine the location of this point. After all, in 3-D, you need 3 pieces of information to determine a specific location.

4. Oct 15, 2014

### LeighV

The thing is I don't even know where to begin with drawing it out...I did attempt to but it never seemed to measure out correctly. @SteamKing it is a really confusing problem because that is the only information they give me, unless I count the north or west measurement as being a 90 degree angle against the axis?

5. Oct 15, 2014

### Staff: Mentor

It's a good question, but before you can answer it you must identify the angle you are interested in. You want the angle between that vector you described and what? Perhaps between that vector and another vector? Or between that vector and the x-y plane?

If the latter, then you are looking for the angle between the vector and its "shadow" on the x-y plane.

This article will get you started. Run through it quickly first, then back up and read more thoroughly. http://www.intmath.com/vectors/7-vectors-in-3d-space.php#anglebetweenvectors