 Hello friends, so we are going to discuss another application of trigonometry in this session and this is called bearings Now you might have wondered while you are traveling By an airplane from point A to point B or from one city to one of the city in what terms or in what terminologies actually the pilots You know talk to their Guides or let's say people were there in the air traffic control So there must be a language which is used You know for by these pilots and navigators so that they can direct their spacecraft or Let's say their aircraft towards that particular location So usually they talk in terms of bearings and that's what we are going to understand What exactly bearings mean and how do we apply them so bearings is a you know tool by which it's a mathematical tool by which We fix location of any given point on our you know on a plane with respect to north direction, right? so We know that you know we have divided the entire plane into four quadrants and the The positive y direction points towards north usually or in a map also north is towards positive conventional positive y direction And then it's east south and west. This is how we have divided the map And now we can locate point P with respect to a north direction by two important values one is called the distance from O To P and second is the bearings. Now bearings is nothing but the angle Made by the line OP. Let's say we are trying to find out the bearings of point P In other words, we want to locate where P point P exactly is with respect to this particular north south east West configuration with O being the origin Let's say O be the central of center of both the north south and east east east west lines Now we want to find out where point P lies Then I have to specify with two data points One is the distance from O to P and second is at what angle The line OP is with respect to any of these reference lines now in bearings case We have taken the reference as the line joining any point towards the north direction. Okay? So that's what is there, you know, so hence North direction is the reference and from that if you measure the angle made by OP Then that is that will be called the bearings For example in this case if I change the location of point P. Let's see point P is here So as you can see if I maintain the distance five units as you can see OP is five But if I change the location of point P the value of alpha this angle This angle is changing. It is 81.47 as of now So as I change in the east direction, it becomes 90 direct 90 degrees That means if someone says that the bearing of a particular point is 90 degrees or You know someone's bearing is 90 degree or an aircraft or a ship's bearing is 90 degrees That means it is heading towards east. Okay, and let's say if I Change the position of P to merge with this direction then alpha is 180 degrees So 180 degrees bearing means someone is heading towards south and now you can figure out that towards best will be 270 degrees and Someone who's heading towards north and we can see say that the bearing of that particular Point or object is zero, right? So zero and Then increases to 90 degree 90. So hence we measure As I told you measure the bearings from positive x positive north direction, right? This is not direction There's no positive negative in north. So positive y direction So from north if you find out the position the angle between the line joining the origin and the north and origin and the point P Origin could be anywhere. It could be one city one location any anywhere in the map, right? And this is that so you draw our Vertically upward direction that is north direction and from that You join the point of which you want to find out the boiling bearing, sorry So hence the the angle made by this north line and the line OP will be the bearing of point P. Okay So as you can see right now the bearing of point P is 56.31 degrees Actually bearings are represented in three digits. So bearings are represented in three digits So for example here bearing of point P with respect to O is 0 5 6 So we usually ignore the decimal part. So 0 5 6 will be the bearing here Now interestingly you can find out bearing of O with respect to P as well So let's try to find that out now You can also see if bearing of point P with respect to O is 56 or 0 5 6 in The way we usually write bearing is three digit one is So three digits before the decimal is considered to be the bearing so 0 5 6 for this and For all with respect to P. So if you want to find out all's bearing with respect to P It's nothing, but it is 236 here. Can you see that so the line? Let's say now P is the origin and this a PA represents the north direction So from this direction P o is making two thirty six point three one degrees So you can you know see it as I'm moving the point P the bearing of O with respect to P also changes. So here if you see Bearing of P with respect to O is 327 But bearing of O with respect to P is 147. Can you see that? So this is what bearing is all about so bearing is nothing but The angle made by the the line joining the origin with that point from the north direction, right? So here also you can see then the angle is taken from north direction only so here 214 is the bearing of O with respect to P and 34 or there is 0 34 is the bearing of P with respect to O now if you can change the Radius also let's say point P is somewhere here or here, but then if you specify the Bearing you know in which direction the particular object is so bearing is nothing but a tool to ascertain this the direction of any particular object with respect to any other point or location, right? So that's what is used extensively in navigation in aircraft or air traffic and you know While ship and move on oceans and things like that. So bearing are important there So in the next session we'll take up a few questions related to bearings and try and understand how Bearings are applied. Thank you