Finding position vectors of x y z in meters

[Sneakatone]

Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude horizontal distance and bearing . suppose an air craft altitude 1450 m , distance 24 km , and bearing 18.0 degrees east of north. what are the x,y,z components in meters of the position vector? the x-axis is east the y-axis is north and the z axis is vertical.


I cannot seem to find the value for x

but I have solved for
y= 22550 m
z=1450 m

 

[tms]

How did you get you y coordinate? If you know y and the distance, how would you find x?

 

[Sneakatone]

I found y by subtracting 24000m by 1450m

 

[tms]

Why do that? 1450 m is the altitude, the z coordinate. It is independent of the horizontal position. Draw a diagram of the x-y plane.

 

[Sneakatone]

is this suppose to make a a triangle? i tried the pythagorean theorem but it dosent seem to work.

 

[tms]

Did you draw the diagram?

You have a vector in the x-y plane with a specified length and direction. You want to find out the x and y coordinates. How do you do that?