Question

what compass heading represents 50° north of east?
?°
hint: compass headings are measured from north, going clockwise.

Explanation:

Step1: Understand Compass Heading

Compass headings start at north (0°) and measure clockwise. East is 90° from north (since north to east is a right angle, 90°).

Step2: Calculate 50° North of East

If we are 50° north of east, we need to find the angle from north. Since east is 90° from north, moving 50° towards north from east means subtracting 50° from 90°? Wait, no. Wait, "north of east" means the angle between the east direction and the line is 50° towards north. So from north, clockwise, east is 90°, so north of east would be 90° - 50°? Wait, no, let's think again. Wait, the hint says compass headings are measured from north, clockwise. So north is 0°, east is 90°, south is 180°, west is 270°. Now, "50° north of east" means the direction is 50° towards north from the east direction. So the angle from north (clockwise) would be 90° - 50° = 40°? Wait, no, that can't be. Wait, no, let's visualize: east is 90° from north (clockwise). If we are 50° north of east, that means the angle between the east axis and the direction is 50° towards north. So from north, going clockwise, to east is 90°, so to get to a direction that's 50° north of east, we start at east (90°) and move 50° towards north (which is counter-clockwise? No, wait, compass heading is clockwise from north. So maybe I got it wrong. Wait, no: "north of east" means the angle is measured from the east direction towards north. So the direction is east, then 50° towards north. So the angle from north (clockwise) would be 90° - 50° = 40°? Wait, no, that seems off. Wait, no, let's take an example: 0° north of east is east (90°). 90° north of east would be north (0°). So 50° north of east should be 90° - 50° = 40°? Wait, no, that can't be. Wait, maybe I mixed up "north of east" and "east of north". Wait, "north of east" is the angle between east and the direction, towards north. So the direction is east + 50° towards north? No, east is 90° from north. If we are 50° north of east, the angle from north is 90° - 50° = 40°? Wait, no, let's use the hint: compass headings are measured from north, clockwise. So north is 0°, east is 90°, south is 180°, west is 270°. So "50° north of east" means that from the east direction, we turn 50° towards north. So the angle from north (clockwise) is 90° - 50° = 40°? Wait, that seems correct. Wait, no, wait: if you are at north (0°), turn clockwise 40°, you are 40° towards east from north, which is 40° east of north. But the question is 50° north of east. Oh! I see my mistake. "North of east" and "east of north" are different. "North of east" means the angle is with respect to east, towards north. So the direction is east, then 50° towards north. So the angle from north (clockwise) is 90° - 50° = 40°? No, that's east of north. Wait, no, let's define:

- "East of north": angle from north towards east. So 50° east of north is 50° from north, clockwise.

- "North of east": angle from east towards north. So to find the angle from north, clockwise, we take east (90°) and subtract the angle north of east (50°), so 90° - 50° = 40°? No, that's not right. Wait, no, let's use coordinates. Let's set north as positive y-axis, east as positive x-axis. A direction 50° north of east means that the angle between the positive x-axis (east) and the vector is 50° towards the positive y-axis (north). So the angle of the vector with respect to the positive y-axis (north) is 90° - 50° = 40°. So the compass heading, which is measured from north (positive y-axis) clockwise (towards positive x-axis, then positive y-axis negative, etc.), so the angle is 40°? Wait, no, clockwise from north: north is 0°, east is 90°, so moving clockwise from north, east is 90°, so a direction that's 50° north of east is 90° - 50° = 40° from north, clockwise. Yes, that makes sense. So the compass heading is 40°? Wait, no, wait, I think I had it backwards. Wait, no, let's take an example: 0° north of east is east (90°). 90° north of east is north (0°). So 50° north of east is 90° - 50° = 40° from north, clockwise. So the compass heading is 40°? Wait, but that seems like east of north. Wait, no, the terminology: "north of east" means the angle is with east as the reference, towards north. So the direction is east + 50° towards north. So in terms of compass heading (from north, clockwise), that's 90° - 50° = 40°. Yes, that's correct.

Answer:

40