Finding position vectors of x y z in meters

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To find the position vector components of an aircraft at an altitude of 1450 m, with a horizontal distance of 24 km and a bearing of 18 degrees east of north, the x, y, and z coordinates need to be calculated. The z coordinate is straightforward as it represents altitude, which is 1450 m. The y coordinate, representing the northward component, has been calculated as 22550 m. To determine the x coordinate, which is the eastward component, a diagram of the x-y plane should be drawn to visualize the triangle formed by the distance and bearing. The Pythagorean theorem can be applied to find the x coordinate once the correct relationships are established.
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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
 
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How did you get you y coordinate? If you know y and the distance, how would you find x?
 
I found y by subtracting 24000m by 1450m
 
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.
 
is this suppose to make a a triangle? i tried the pythagorean theorem but it dosent seem to work.
 
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?
 

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