 Hello and welcome to the session let us discuss the following question it says the angle of depression of the top and the bottom of a building 50 meters high as observed from the top of a tower are 30 degrees and 60 degrees respectively find the height of the tower and also the horizontal distance between the building and the tower. So we are given a building which is 50 meter high as the angle of depression from the top of the tower to the top and the bottom of the building are 30 degrees and 60 degrees respectively right. So this angle is 30 degrees because it is the angle of depression from the tower to the top of the building and this angle is 60 degrees so this is the angle from the top of the tower to the bottom of the building. So if this angle is 30 degrees this angle will also be 30 degrees because horizontal line through the top of the tower is parallel to this line and similarly this angle will be 60 degrees. So let us name these points as A, B, C, D let us now move on to the solution we have to find the height of the tower so let AC be the tower, 6 meter high we are given that ED is the building which is 50 meter high now ED is 50 meter so BC is also 50 meter will be equal to X minus 50 because the height of the tower is 50 meter that is AB is equal to AC minus BC so this is equal to X minus 50 meter why meter be the distance between CD is the distance between and the building and this is we have assumed as Y meter CD is same as EV we have perpendicular upon base is equal to tan 30 degrees perpendicular is AB upon base which is EV is equal to tan 30 degrees AB is X minus 50 and EV is Y and tan 30 degrees is 1 upon root 3 so this implies root 3 into X minus 50 is equal to Y and this implies root 3 X minus 50 into root 3 is equal to Y and this implies root 3 X minus Y is equal to 50 into root 3 let us name this equation as 1. Now in right triangle ACD we have perpendicular upon base is equal to tan 60 degrees perpendicular is AC which is X upon CD which is Y meter is equal to tan 60 degrees now tan 60 degrees is root 3 so this is equal to root 3 so this implies X is equal to root 3 Y let's take this as 2 now using 1 and 2 now this will substitute X is equal to root 3 Y in equation 1 root 3 X that is root 3 into root 3 Y minus Y is equal to 15 to root 3 now root 3 into root 3 is 3 so 3 Y minus Y is equal to 50 into root 3 3 Y minus Y is 2 Y is equal to 15 to root 3 so this implies Y is equal to 25 into root 3 now from 2 we have X is equal to root 3 Y so X is equal to root 3 into Y Y is 25 into root 3 so it becomes root 3 into root 3 is 3 it becomes 25 into 3 which is equal to 75 so this implies at the height of the tower equal to 75 meter and the horizontal distance between tower and the building is equal to 25 into root 3 meters so this completes the question and the session I for now take care have a good day