 Hello and welcome to another problem solving session on triangles. In this session we have taken up the problem which is shown on the screen. So what does the question say? The question says a vertical stick of 12 meter long, a vertical stick 12 meter long casts a shadow 8 meter long on the ground. At the same time a tower casts the shadow 40 meter long on the ground, determine the height of the tower. So hence let us try and understand the process of shadow making. So let us say this is the sun or any source of light and because of that let us say this is the stick and this is 12 meter long and let us say the shadow is 8 meter long. So let me just name these. So let us say the stick was AB and the shadow is BC. So given AB is equal to 12 meters and BC the shadow is 8 meters. Now there is another tower which is long enough whose shadow, so you know the light rays fall like that and hence the shadow is created. The light rays fall on this and in fact I should have shown you like this because the sun will be in that direction from where, so this is the source of light let us say. So this is how light is falling on the ground and hence. So sun's position would be somewhere on top so I am not showing that. Now similarly there is a tower and the towers, that is a shadow is this and let me join these and this is ABCDEF okay, DEF. Now this is given to be equal to 40. What is 40? Shadow 40 meter long, so EF is 40 meter long okay. So we have to find out what? H correct. Now if you see this is a very practical problem and how do we approach it? So clearly the stick as well as the tower is perpendicular to the ground. So this is 90 degree and the inclination of the sun will be same is it at the same time during the day the theta angle, whatever the theta angle is will be the same because the sun is at the same height for every object right. So hence in this case also the sun rays would be falling like that and hence the shadow is forming like that isn't it? So inclination of the sun, sun is somewhere here let us say in the horizon okay. So hence this is the clear cut question of similar triangle. So if you see in triangle ABC and triangle DEF what do we get? Angle ABC is equal to angle DEF is equal to 90 degree each and angle ACB is equal to angle DFE and why is that? Inclination to sun both are inclination of sun correct or angle of elevation of sun whichever way you want to say. Let me write it here now therefore triangle ABC is similar to triangle DEF and what is that? Reason being by AA similarity right by AA similarity. So this is done. So the moment this is done I can say AB by AB by DE is equal to BC by EF. Why is that? This is nothing but corresponding parts of similar triangles are proportional right. So ratio of these sides will be proportional. So now I have to find out DE isn't it? So DE clearly is equal to BC sorry AB into EF upon BC and let us find out the values. So AB is how much? AB was 12 meters into EF. EF is 40 meters divided by BC. BC was 8 okay. So this is nothing but this will go 5 times so it is 60 meters. So you can say the height of the tower is 60 meters. So you know now you know how to find out the height of an object. So it is very easy to find a stick with a known length and its shadow and also you can find the distance between foot of the foot of the let us say building and a particular point or let us say the length of the shadow the moment it is done you can find out the height of the building correct without even trying to climb the building right. So you do not need to climb the building and yet you will be able to or the tower you will be able to find out the height of the tower is it it? So this is so interesting application area of similar triangles.