 Hello and welcome to the session. I am Deepika here. Let's discuss a question from a point on the ground the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 meter high building are 45 degree and 60 degree respectively. Find the height of the tower. Let us first understand the angle of elevation. In this figure qr is a horizontal line. The angle of elevation from q turned by pq with qr that is here the angle of elevation is angle pqr. So this is a key idea. We find that question. We will take the help of this key idea to solve our question. So let's start the solution. First we will draw a simple diagram to represent our problem here. In this diagram pt represents a transmission tower and qt is a building which is 20 meter high. Now the angle of elevation of p from r is 60 degree and angle of elevation of t from r is 45 degree. So we have given qt is equal to 20 meter and angle trq is equal to 45 degree. Now in right triangle rq we have now we want to find rq. So we will use a trigonometric ratio which involves both tq and rq and that is 1045 degree. Here for tq upon rq is equal to 1045 degree. So we have now tq is given to us 20 meter 20 over rq is equal to 1045 degree and this is 1. So this implies rq is also equal to 20 meter. Again in right triangle prq we have rq is equal to 20 meter. The height of the tower is h meter. Therefore q is equal to 20 plus h meter. Again angle prq is equal to 60 degree. Now we want to find pq. So we have pq upon rq is equal to 1060 degree. Now pq is 20 plus h meter upon rq is 20 meter is equal to root 3 as 1060 degree is root 3. Now on cross multiplication we have 20 plus h is equal to 20 root 3. So we have h is equal to 20 root 3 minus 20 and this is equal to 20 into root 3 minus 1. Hence the height of the tower is 20 into under root 3 minus 1 meter. Hence the answer for the above question is 20 into under root of 3 minus 1 meter. I hope the solution is clear to you. Bye and take care.