Hi, students, in this module from the chapter 4 of Trigonometry, lets learn the application of Trigonometry.

Now students, we have already learnt the ratios of Trigonometry, right, now when is this Trigonometry going to be applied in real life that is what we are going to learn now, observe now. So for this we are going to take a few examples. Now observe, there is a person here, and standing and watching Mount Everest and he is wondering something. He is thinking, what is the height of Mount Everest, and the next is how will I measure it. The question is, is he going to take a measuring tape, fix one end to the top and take the next end to the bottom and measure it. No, it is not possible that means it is impossible to measure it with the help of a measuring tape, isn’t it. The same way you observe this, now there is a person here, there is a boy standing here and observing this river, and he is thinking what is the width of this river, right. Is he going to take a measuring tape and do the same thing like that person did. No, it cannot be, it is impossible to do it with the help of a measuring tape to get the width of the river, right.

In the same way, here you have a couple standing and observing Eiffel Tower, right, and they are conversing between themselves. They are saying, yeah, it is looking beautiful, right. Yes, she says, yes, it is looking beautiful. But I am wondering what is its height? He is saying, oh, yeah, what is its height, how do we measure it. The same question they have. They are not again going to take the help of a measuring tape, it cannot be done, that means it is impossible to do it with the help of a measuring tape. So in all these three cases when you look, like the first case where we saw the height of the Mount Everest, second case when we talk about the width of the river and third case when we talk about the height of the Eiffel Tower. All such big heights and distances can be actually practically taken and we can find it out with the help of applying trigonometry. So application that is real application of trigonometry.

And if we have to learn this, students there are a few terms which we need to know, very important terms. There are basically four terms, first term is line of vision, second is horizontal line, third is angle of elevation and fourth is angle of depression. Now for this we have got a friend of ours and he is Raj, he is going to help us, he is saying, yeah, hi, I am going to help you to learn all the four terms, let’s understand. He is going to help us with the first term here, observe. So here comes Raj and what is he observing, he is observing a cow. So when he is observing a cow here, this person Raj becomes the observer and this cow becomes the object. When this observer is observing the object, there is a line passing through his eye connecting to that object. This imaginary line which connects the eye of the observer to the object is called Line of Vision. So that means the moment an observer observes an object there is a straight line passing through his eye to that object, that straight line is called as ‘Line of Vision’. Beautiful isn’t it, so easy.

In the same way, let’s see Raj is going to observe something more, what is he observing. Yes, this time see he is seeing the door of that tree house, see he is seeing the door of the tree house, he is seeing that. So now Raj is observer, that door is the object. So, the straight line connecting his eye to the object that is nothing but is the ‘Line of Vision’, beautiful. Let’s see, he is going to see a few more examples. What is he doing? Yeah, this time what is he seeing? He is seeing the beautiful flowers on the ground there. So now he is the observer and that flower is the object that straight line is nothing but again, you know, it is line of vision. Isn’t that easy?

Now Raj is going to do something more interesting, what is he doing? Yes, he is saying I want that apple, which apple, yes, that apple there on the tree. Now Raj is the observer and that apple is the object. So the straight line connecting his eye to that object is the ‘Line of Vision’. So this is what we say, so we understood what is Line of Vision, it is so very simple, wherever an observer observes an object, the line connecting his eye to the object is called Line of Vision. And that is the concept, isn’t that easy, the first concept we have learnt it, very simple.