Weird question in "Vectors" chapter

[Rijad Hadzic]

Homework Statement

Two aircraft approaching an aircraft carrier are detected by radar. The first aircraft is at a horizontal distance of 34.3 km in the direction 42 deg north of east. and has altitude 2.4 km

The second aircraft, at altitude 1.2 km, is at horizontal distance of 42.6 km in the direction 37 deg north of east.

What is the distance separating the two aircraft? Hint: use a coordinate system with the x-axis pointing east, the y-axis pointing north, and the z axis in the vertical direction

Homework Equations

The Attempt at a Solution

Ok I really don't understand the hint. it says the z axis in the vertical direction, correct me if I'm wrong but isn't north the vertical direction, which they said make the y axis?

And why do you even need an axis for this problem? Same with the angles.

I used the distance formula: $((x_2 - x_1)^2 + (y_2 - y_1)^2 )^{1/2}$

plugging 42.6 as x_2 and 34.3 as x_1, 1.2 for y_2 and 2.4 for y_1

and got answer 8.38 km.

Book says answer is 9.02 km.

My doubts here are: first off, why would I need to use a 3 dimensional axis?

Second off, I used arc tan to check the angles and they seem off.

For example, on aircraft 1 I did arctan(2.4/34.3) and got 4 degrees, not even close to their stated 42 degrees.

Anyone have any clue? My book is starting to piss me off cause if you've been following the last two questions I asked on here apparently my book was wrong as well, I really want to complain to the author and I question why this was used in an introductory physics course cause I don't feel like I'm learning the material right because of all the contradictions.

Sorry for venting just had to get that off of my chest, and if i am indeed wrong I'm just going to look dumb for complaining lol.

Anyways can anyone please help me.

 

[J Hann]

Say then, you use the x and y coordinates in the horizontal plane to describe the displacements (from the origin).
How can you describe the altitude without using a z (vertical axis)?

 

[Rijad Hadzic]

Say then, you use the x and y coordinates in the horizontal plane to describe the displacements (from the origin).
How can you describe the altitude without using a z (vertical axis)?

Wouldn't horizontal distance be on the x-axis and altitude be vertical distance?

 

[cnh1995]

first off, why would I need to use a 3 dimensional axis?

Because you've been given the locations in 3 dimensions.

correct me if I'm wrong but isn't north the vertical direction, which they said make the y axis?

Imagine yourself standing on the ground facing north. So, y-axis is going straight ahead (along north), x-axis is going to your right (east) and z axis is going towards the sky (vertically upward).

 

[Rijad Hadzic]

Because you've been given the locations in 3 dimensions.

Imagine yourself standing on the ground facing north. So, y-axis is going straight ahead (along north), x-axis is going to your right (east) and z axis is going towards the sky (vertically upward).

alright I think I'm starting to get it. I'm going to work it again and come back if I need any help..

 

[Rijad Hadzic]

Looks like I'm going to have to use the distance formula with 3 variables..

 

[Rijad Hadzic]

Got the correct answer guys.

Main thing I learned this problem:

I have a one track thought, I need to try harder to dig for the answer. They even gave me a hint yet I still thought that my way was right. I need to stop looking for help and basically try to understand the question better on my own.