 Hi and welcome to the session. Today we will learn some applications of trigonometry. We will learn how to use trigonometry to find out heights and distances of various objects without actually measuring them. So first of all let us see what is line of sight. Let us understand this with the help of a figure. Here suppose we have a observer and we have marked the height of the observer as ct and we have an object whose height is av. The line ca which is drawn from the eye of the observer to a point on the object which is viewed by the observer is known as the line of sight. So here we can write that the line of the sight is the line drawn from the eye of an observer to the point in the object viewed by the observer. Now let us see what is angle of elevation. In this figure the observer cd looks at the object av from the point c. So for this the horizontal line will be ce. Now when the observer is looking at a point which is above the horizontal level then the angle of elevation will be the angle formed by the line of sight and the horizontal level. That means this is angle of elevation. So the angle of elevation of the point being viewed is the angle by the line of sight with the horizontal when the point being viewed is above the horizontal level. Now let us see angle of depression. Now suppose av is the observer and here we have an object which we have named as c then ac that is the line from the eye of the observer to the object will be the line of sight and this will be the horizontal level or horizontal line for the observer that is the level from where the observer looks at the object. So when the observer looks at the object which is below the horizontal level then the angle of depression is the angle formed by the line of sight with the horizontal level. So this is an angle of depression thus angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level the height length of an object or the distance between two objects can be determined with the hell trigonometric ratios that is we can find the length of ab or bc or ca with the help of some information given to us and with the help of trigonometric ratios. So let's see one small example for that suppose we are given a tower ab now from a point on the ground 20 meter away from the foot of a vertical tower say here the angle of elevation of the top of the tower is 60 degrees. So this angle of elevation is 60 degrees now the point c from the foot of the tower that is b is 20 meter away so cb is 20 meters now we need to find the height of the tower now for the angle c ab is the perpendicular cb is the base and ac is the hypotenuse and we know that tan 60 degrees will be equal to perpendicular base so this implies tan 60 degrees is equal to perpendicular that is ab upon base that is cb now tan 60 is root 3 so root 3 is equal to ab upon cb that is 20 meters on cross multiplying we get ab equal to 20 root 3 meters so the height of the tower is 20 root 3 meters so this is how we use the trigonometric ratios and the information given to us to find out the height of the tower I hope all the concepts must be clear to you with this we finish this session goodbye take care and have a nice day