what compass heading represents 20° north of west? ?° hint: compass headings are measured from north, going…

Explanation:

Step1: Understand Compass Heading

Compass headings are measured clockwise from north. West is 270° from north (since north is 0°, east is 90°, south is 180°, west is 270°). But we need 20° north of west, so we adjust from west towards north.

Step2: Calculate the Heading

North is 0°, west is 270°. Moving 20° north from west means we subtract 20° from 270°? Wait, no. Wait, if we are at west (270°), and we go 20° towards north (which is clockwise? Wait, no, north of west: from west, towards north. But compass heading is clockwise from north. So north is 0°, west is 270°. To find 20° north of west, we need to see the angle from north, clockwise. West is 270° from north. North of west means towards north from west, so the angle from north would be 180° - 20°? Wait, no. Wait, let's think again. North is 0°, east is 90°, south is 180°, west is 270°. If we are 20° north of west, that means from west, we turn 20° towards north. But in terms of clockwise from north, west is 270°, so moving towards north (which is counter - clockwise from west) but compass heading is clockwise from north. Wait, maybe a better way: the angle between north and the direction is 180° - 20°? No, wait. Let's draw a mental picture. North is up, west is left. 20° north of west means the direction is 20° towards north from the west direction. So from the north axis, clockwise, west is 270°, so to get 20° north of west, we need to go 180° - 20°? No, wait, no. Wait, the standard compass heading: 0° is north, 90° is east, 180° is south, 270° is west. If we have a direction that is 20° north of west, that means the angle between the north - south line (north) and the direction is 20° towards west? No, no. Wait, "north of west" means the direction is closer to north than to west. So from the west direction, we turn 20° towards north. So the angle from north, clockwise: north is 0°, west is 270°, so 20° north of west would be 180°+ (90° - 20°)? Wait, no. Wait, let's consider the angle between the north vector and the desired vector. If we are 20° north of west, the angle between the north - axis (0°) and the desired direction, measured clockwise, is 180° - 20°? No, that's not right. Wait, let's use the formula: for a direction that is $\theta$ degrees north of west, the compass heading (measured clockwise from north) is $180^{\circ}+\left(90^{\circ}-\theta\right)$? No, wait, west is 270°, so 20° north of west is 270° - 20° = 250°? Wait, let's check with an example. If it's 0° north of west, that's west, which is 270°. If it's 90° north of west, that's north, which is 0°. So as we increase the angle north of west from 0° to 90°, the compass heading (clockwise from north) decreases from 270° to 0°. So the formula is: compass heading = 270° - $\theta$, where $\theta$ is the angle north of west. So here, $\theta = 20^{\circ}$, so compass heading = 270° - 20° = 250°.

Answer:

250