Question

what compass heading represents 45° east of south? ?° hint: compass headings are measured from north, going clockwise.

Explanation:

Step1: Understand compass heading

Compass headings are measured clockwise from north. South is 180° from north (since north is 0°, east is 90°, south is 180°, west is 270°).

Step2: Calculate 45° east of south

To find 45° east of south, we start at south (180°) and move 45° towards east (clockwise). So we add 45° to 180°? Wait, no. Wait, south is 180°, east of south means towards east from south. Wait, north is 0°, east is 90°, south is 180°, west is 270°. So from north, clockwise: north (0°), east (90°), south (180°), west (270°), back to north (360°). Now, 45° east of south: south is 180°, east of south is towards east, so we need to go 45° towards east from south. But since we measure from north clockwise, let's think: from north to south is 180°, then east of south is 45° towards east. So total heading is 180° + 45°? Wait, no. Wait, south is 180°, east is 90°, so between south (180°) and east (90°)? No, wait, east is 90°, south is 180°, so east of south is between south (180°) and east (90°)? No, that can't be. Wait, no: "east of south" means the direction is south, then 45° towards east. So from the south direction, turn 45° towards east. Now, compass heading is measured from north, clockwise. So north (0°), east (90°), south (180°), west (270°). So to get the heading for 45° east of south, we can calculate as follows: The angle from north to south is 180°, then from south to the direction 45° east of south is 45° towards east (which is towards decreasing the angle from north? Wait, no. Wait, if we are at south (180°), and move 45° towards east, that is towards the direction of east, which is 90° from north. Wait, maybe a better way: the standard position for compass headings: 0° is north, 90° is east, 180° is south, 270° is west. So "45° east of south" means the direction is 45° towards east from the south direction. So the angle from north would be: south is 180°, and then 45° towards east (which is towards the direction of east, so from south, turning towards east (clockwise) by 45°). Wait, but east is 90°, so south is 180°, east of south is between south (180°) and east (90°)? No, that's west of south. Wait, no: "east of south" means the direction is south, then偏向east, so the angle between the south line and the direction is 45° towards east. So in terms of compass heading (measured from north, clockwise), let's draw this: north (0°), east (90°), south (180°), west (270°). The direction 45° east of south: start at south (180°), then turn 45° towards east (which is towards the left if we face south, but in compass heading, we measure clockwise from north). So from north, clockwise, the angle to this direction: north to south is 180°, then from south, turning 45° towards east (which is towards the direction of east, so the angle from north would be 180° - 45°? No, that doesn't make sense. Wait, no: if you are at south (180°), and turn 45° towards east, that is towards the direction of east, which is 90° from north. So the angle from north to this direction would be 180° - 45°? Wait, no, that would be 135°, but 135° is southeast (45° east of south? Wait, no: 45° east of south is the same as southeast? Wait, southeast is 45° east of south (or 45° south of east). Wait, southeast is 135° from north? Wait, no: north (0°), east (90°), southeast is halfway between east (90°) and south (180°), so (90° + 180°)/2 = 135°. Oh! Wait, that's correct. So southeast is 135° from north, which is 45° east of south (since from south, 45° towards east is southeast, which is 135° from north). Wait, but the problem says 45° east of south. Wait, let's re-express:

Compass heading is measured clockwise from north. So:

- North: 0°

- East: 90°

- South: 180°

- West: 270°

Now, "45° east of south" means the direction is south, then 45° towards east. So to find the heading, we can think of it as: from north, go clockwise to south (180°), then go 45° towards east (but east is towards decreasing the angle from north? No, wait, east is 90°, south is 180°, so between east (90°) and south (180°) is the southeast quadrant. The angle for southeast (45° east of south and 45° south of east) is 135°, because from north, clockwise: 0° (north), 90° (east), 135° (southeast), 180° (south), 225° (southwest), 270° (west), 315° (northwest), 360° (north). Wait, that makes sense. So 45° east of south is the same as southeast, which is 135° from north? Wait, no, wait: 45° east of south: south is 180°, east of south is towards east, so the angle from north would be 180° - 45° = 135°? Wait, no, 180° - 45° is 135°, but if we are at south (180°) and move 45° towards east, that is towards the direction of east (90°), so the angle from north would be 180° - 45° = 135°? Wait, but 135° is between east (90°) and south (180°), which is southeast. So yes, 45° east of south is 135°? Wait, no, wait, maybe I got it wrong. Let's use the hint: compass headings are measured from north, going clockwise. So north is 0°, clockwise. So to find 45° east of south, let's break it down:

- South is 180° (since 0° north, 90° east, 180° south, 270° west).

- "East of south" means the direction is south, then 45° towards east. So from the south direction (180°), we turn 45° towards east (which is clockwise? Wait, no: east is to the left of south if you are facing south. Wait, if you face south, east is to your left, west to your right. But compass heading is measured clockwise from north, so east is 90°, south is 180°, so clockwise from north: north (0°), east (90°), south (180°), west (270°). So to get the heading for 45° east of south, we need to calculate the angle from north, clockwise, to that direction.

Let's consider the standard position:

- North: 0°

- East: 90°

- South: 180°

- West: 270°

The direction 45° east of south: the angle between the south axis (180°) and the direction is 45° towards east. So the angle from north is 180° - 45° = 135°? Wait, no, that would be if we go counterclockwise from south to east, but we need to go clockwise from north. Wait, maybe a better approach: the total angle from north to the direction is the angle from north to south (180°) plus the angle from south to the direction towards east? No, that can't be, because east is 90°, which is less than 180°. Wait, I think I made a mistake earlier. Let's use the formula for compass headings:

A direction of \( \theta \) degrees east of south means that the angle from the south axis towards east is \( \theta \) degrees. To find the compass heading (measured from north, clockwise), we can use the following:

- South is 180° from north.

- East of south means we are moving towards east (which is a direction of decreasing angle from north, since east is 90°). Wait, no, east is 90°, which is less than 180°, so from south (180°), moving towards east (90°) is moving counterclockwise? But compass headings are measured clockwise. Wait, this is confusing. Let's use a diagram:

- North (0°) at the top, east (90°) on the right, south (180°) at the bottom, west (270°) on the left.

- "45° east of south" means the direction is south (bottom), then 45° towards east (right). So in the diagram, from the bottom (south), turn 45° towards the right (east). Now, the compass heading is the angle from the top (north) clockwise to this direction.

So from north (top), clockwise to east (right) is 90°, to south (bottom) is 180°, to west (left) is 270°. Now, the direction 45° east of south is in the southeast quadrant, 45° from both south and east. So the angle from north clockwise to this direction is 180° - 45° = 135°? Wait, no, 180° - 45° is 135°, but if we are at south (180°) and move 45° towards east (right), the angle from north would be 180° - 45° = 135°, which is correct because southeast is 135° from north (45° east of south and 45° south of east). Wait, but let's check with the hint: compass headings are measured from north, going clockwise. So north (0°), clockwise: 0° (north), 90° (east), 135° (southeast), 180° (south), 225° (southwest), 270° (west), 315° (northwest), 360° (north). Yes, that makes sense. So 45° east of south is the same as southeast, which is 135° from north. Wait, but wait, 45° east of south: the angle from south towards east is 45°, so the heading is 180° - 45° = 135°? Wait, no, that would be if we subtract, but let's think of it as: from north, clockwise, the angle to south is 180°, then to get to 45° east of south, we need to go 45° towards east from south, but east is at 90°, so the angle from north is 180° - 45° = 135°. Yes, that's correct. So the compass heading is 135°.

Step3: Verify

Let's verify: north (0°), east (90°), southeast (135°), south (180°), southwest (225°), west (270°), northwest (315°), north (360°). So 45° east of south is southeast, which is 135° from north. So the answer should be 135.

Answer:

135