Question

what compass heading represents 25° west of north?
?°
hint: compass headings are measured from north, going clockwise.

Explanation:

Step1: Understand Compass Heading

Compass headings are measured clockwise from north. North is \(0^\circ\) (or \(360^\circ\)). When we go west of north, we are moving clockwise from north towards west, but the angle west of north is the deviation from north towards west. Wait, no—wait, the standard compass heading: if it's \(x^\circ\) west of north, the heading (measured clockwise from north) would be \(360^\circ - x^\circ\)? Wait, no, wait. Wait, north is \(0^\circ\) (or \(360^\circ\)), east is \(90^\circ\), south is \(180^\circ\), west is \(270^\circ\). But when we say \(25^\circ\) west of north, that means from north, we turn \(25^\circ\) towards west (which is counter - clockwise? No, wait the hint says compass headings are measured from north, going clockwise. Wait, no—wait, the hint says "Compass headings are measured from north, going clockwise." So north is \(0^\circ\), then as we turn clockwise, we go towards east ( \(90^\circ\) ), south ( \(180^\circ\) ), west ( \(270^\circ\) ). But "west of north"—if we are west of north, that is towards the left of north (counter - clockwise), but the heading is measured clockwise from north. Wait, maybe I got it wrong. Wait, no—let's think again. The standard compass heading: a heading of \(0^\circ\) is north, \(90^\circ\) is east, \(180^\circ\) is south, \(270^\circ\) is west. But when we say \(x^\circ\) west of north, that means the angle between north and the direction is \(x^\circ\) towards west. But since heading is measured clockwise from north, to get the heading for \(x^\circ\) west of north, we need to calculate \(360^\circ - x^\circ\)? Wait, no, that can't be. Wait, no—if you are at north (\(0^\circ\)) and turn clockwise towards west, you are moving towards \(270^\circ\), but \(25^\circ\) west of north—wait, maybe the question is a bit tricky. Wait, no, maybe I misinterpret. Wait, the hint says "Compass headings are measured from north, going clockwise." So north is \(0^\circ\), then as we go clockwise, we go to east (\(90^\circ\)), south (\(180^\circ\)), west (\(270^\circ\)). But "west of north"—if it's \(25^\circ\) west of north, that means the direction is \(25^\circ\) towards west from north. But when measuring clockwise from north, the angle for west of north: wait, no—if you are facing north, and turn \(25^\circ\) towards west (which is counter - clockwise), but the heading is measured clockwise. Wait, maybe the question has a typo? No, wait, maybe I'm overcomplicating. Wait, no—wait, the standard way: when we say \(x^\circ\) west of north, the compass heading (measured clockwise from north) is \(360^\circ - x^\circ\)? No, that would be if it's \(x^\circ\) east of north, it's \(x^\circ\), \(x^\circ\) south of east, it's \(90^\circ + x^\circ\), etc. Wait, no—let's take an example. If it's \(0^\circ\) west of north, that's north, heading \(0^\circ\). If it's \(90^\circ\) west of north, that's west, heading \(270^\circ\). So the formula is: heading = \(360^\circ - x^\circ\) when it's \(x^\circ\) west of north? Wait, no, \(360 - 90 = 270\), which matches. \(360 - 25 = 335\). Wait, that makes sense. Because north is \(0^\circ\), east is \(90^\circ\), south is \(180^\circ\), west is \(270^\circ\). So if you are \(25^\circ\) west of north, you are \(25^\circ\) towards west from north. So the clockwise angle from north would be \(360^\circ - 25^\circ=335^\circ\).

Step2: Calculate the Heading

Given the angle west of north is \(25^\circ\), and compass heading is measured clockwise from north. So we subtract the west - of - north angle from \(360^\circ\) (since west is \(270^\circ\), and \(25^\circ\) west of north is \(25^\circ\) towards west from north, so the clockwise angle is \(360 - 25 = 335\) degrees.

Answer:

\(335\)