Question

what compass heading represents 19° 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 \(360^\circ\)). West of north means we are moving towards the west direction from north, but since we measure clockwise, we need to consider the angle from the north axis towards the west (which is a counter - clockwise direction from the east - west axis, but the hint says we measure clockwise from north). Wait, actually, when we say \(x^\circ\) west of north, in terms of clockwise measurement from north, the angle is \(360^\circ - x^\circ\)? No, wait, no. Wait, north is \(0^\circ\) (or \(360^\circ\)). If we are west of north, the clockwise angle from north would be \(360^\circ- 19^\circ\)? No, that's not right. Wait, let's think again. The standard compass heading: North is \(0^\circ\) (or \(360^\circ\)), east is \(90^\circ\), south is \(180^\circ\), west is \(270^\circ\). When we say \(19^\circ\) west of north, we start at north (\(0^\circ\)) and turn \(19^\circ\) towards the west (which is the counter - clockwise direction from the positive x - axis (east) perspective, but the hint says we measure clockwise from north). Wait, no, the hint says "Compass headings are measured from north, going clockwise". So north is \(0^\circ\), and as we turn clockwise, we go towards east ( \(90^\circ\)), then south (\(180^\circ\)), then west (\(270^\circ\)), then back to north (\(360^\circ\)). So if we are \(19^\circ\) west of north, that means from the north direction, we turn \(19^\circ\) towards the west, but since we measure clockwise, the angle would be \(360^\circ - 19^\circ=341^\circ\)? Wait, no, that can't be. Wait, maybe I got the direction wrong. Let's take a simple example: \(0^\circ\) is north. \(10^\circ\) east of north would be \(10^\circ\) clockwise from north (towards east), so the heading is \(10^\circ\). \(10^\circ\) west of north would be \(360^\circ - 10^\circ = 350^\circ\) clockwise from north? Wait, no, that's not correct. Wait, actually, when you are west of north, the clockwise angle from north is \(360^\circ - \theta\), where \(\theta\) is the angle west of north. Wait, let's use the standard formula: The compass heading \(H\) for an angle \(\theta\) west of north is given by \(H = 360^\circ-\theta\). So for \(\theta = 19^\circ\), \(H=360 - 19=341^\circ\)? Wait, no, that seems off. Wait, no, maybe I have the direction reversed. Let's think of the coordinate system: North is along the positive y - axis. East is positive x - axis. Clockwise from north: the angle increases as we move towards east (positive x - axis). So if we are west of north, we are moving towards the negative x - axis direction from the positive y - axis. So the angle clockwise from north would be \(360^\circ - 19^\circ=341^\circ\)? Wait, but let's check with a smaller angle. Suppose \(1^\circ\) west of north. Clockwise from north, the angle should be \(359^\circ\), which is \(360 - 1\), so that makes sense. So for \(19^\circ\) west of north, the clockwise angle from north is \(360-19 = 341^\circ\). Wait, but let's confirm with the hint. The hint says "Compass headings are measured from north, going clockwise". So starting at north (\(0^\circ\)), turning clockwise (towards east) gives angles from \(0^\circ\) to \(90^\circ\) (east), \(90^\circ\) to \(180^\circ\) (south - east to south), \(180^\circ\) to \(270^\circ\) (south - west to west), \(270^\circ\) to \(360^\circ\) (north - west to north). So when we are west of north, we are in the \(270^\circ\) to \(360^\circ\) range. The angle west of north is the angle between the north line and the line towards the west - north direction, measured towards the west (counter - clockwise from the north line). But since we measure clockwise from north, the angle is \(360^\circ-\text{angle west of north}\). So for \(19^\circ\) west of north, the clockwise angle from north is \(360 - 19=341^\circ\).

Step2: Calculate the Heading

Given that the angle west of north is \(19^\circ\) and we measure clockwise from north, the compass heading \(H\) is calculated as \(H=360^\circ - 19^\circ=341^\circ\).

Answer:

\(341\)