 Hello and welcome to the session. In this session I will discuss a question which says that from the top of the 7 meters high building, the angle of elevation of the top of the tar is 60 degrees and the angle of depression of the foot of the tar is 30 degrees. Find the height of the tar. Now before starting the solution of this question we should know some results. First is in triangle ABC, tan theta is equal to perpendicular over base which is equal to AB over BC. As the perpendicular here is AB and base here is BC. And second is the angle of elevation. Now suppose a person is standing at a point A and he is observing an object which is at the point C. Then in this case AC will become the line of sight. Now the angle found between the line of sight and the horizontal that is this angle which is angle BC is called the angle of elevation. So here angle of elevation is angle BC. And third is the angle of depression. Now in this case suppose a person is standing on the top of the tar AB that is at point A and he is viewing an object which is lying at the point C. Then in this case AC will be the line of sight and the angle which is found between the line of sight and the horizontal that is this angle is called the angle of depression. So here angle of depression is angle DAC. So the angle of depression is formed whenever the object is lying below the horizontal level that is the case when we lower our head to look at the point being viewed. Now these results will work out as a key idea for solving out this question. Now we will start with the solution. Now let AB be the building and CE be the tar. Now it is given that from the tar at the 7 meters high building the angle of elevation of the top of the tar is 60 degrees and angle of depression of the foot of the tar is 30 degrees. Now using this result which is given in the key idea from the top of the building the angle of elevation of the top of the tar is equal to 60 degrees. So we have angle EDD is equal to 60 degrees. Now using this result which is given in the key idea from the top of the building the angle of depression of the foot of the tar is 30 degrees. So we have angle TKC is equal to 30 degrees. Now from the diagram AD is parallel to BC therefore angle CKD is equal to angle ACP as these are interior alternate angles. So this implies angle ACB is equal to 30 degrees that is this angle is equal to 30 degrees. Now using this result which is given in the key idea in triangle ABC tan 30 degrees is equal to AB over BC which is perpendicular over place. Now this implies tan 30 degrees which is 1 by root 3 is equal to AB which is 7 over BC which further implies BC is equal to 7 root 3 meters. Now from the diagram AD is equal to BC therefore AD is also 7 root 3 meters. Now in triangle AD tan 60 degrees is equal to ED over AD. Now this implies tan 60 degrees is root 3 is equal to ED over AD and AD is 7 root 3 meters so it will be 7 root 3 which implies ED is equal to 7 root 3 into root 3 meters which is equal to 7 into 3 meters which is equal to 21 meters. So we have ED is equal to 21 meters. Also from the diagram AB is equal to CD is equal to 7 meters. So here CD is equal to 7 meters. Now EC is equal to ED plus DC as you can see from the diagram EC is equal to ED plus DC. Now this is equal to ED is equal to 21 meters plus DC is equal to 7 meters which is equal to 28 meters. Now we have taken CD as the tar hence height of the tar that is EC or CE is equal to 28 meters. So this is the solution of the given question and that's all for this session hope you all have enjoyed the session.