 Hi and welcome to the session. Today I will help you with the following question which says a statue 1.46 meter tall stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of the statue is 60 degrees and from the same point the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the pedestal. Use root 3 is equal to 1.73. Now before moving on to the solution let us recall view points. First of all for any angle theta tan theta is equal to perpendicular upon base second tan of 45 degrees is equal to 1 and tan of 60 degrees is equal to root 3. So in this question these three points will work as the key idea. Now let's see its solution. First of all let us make the required figure according to the given question. So here this is the required figure. This is the pedestal and the statue stands on the top of the pedestal which is 1.46 meter tall. Now here is the point on the ground same point P and from this point P on the ground the angle of elevation of the top of the statue is 60 degrees. So that means this angle is 60 degrees and the angle of elevation of the top of the pedestal is 45 degrees. So here this angle is 45 degrees and we need to find the height of the pedestal. So let us assume that the height of the pedestal be h meters. Now let us name this point as A this as B and this as C. So here P A is the distance between the point P on the ground and the bottom of the pedestal. So let us assume that it is times P A is x meters. Thus here we have A B as the height of the pedestal which we assumed to be h meters. B C is the height of the statue which is given to be 1.46 meters. P is the point on ground. Here angle B P A is the angle of elevation of the top of the pedestal which is equal to 45 degrees and angle C P A is the angle of elevation of the top of the statue which is given to be 60 degrees. And lastly we have assumed that the distance P A is equal to x meters. Now the angle between the pedestal and the ground is a right angle. So that means triangle B P A and triangle C P A are both right-angled triangles. So first of all consider the right triangle P A B so in right triangle P A B angle B P A is given to be 45 degrees and we know the tan theta is equal to perpendicular upon base. So let us take theta as 45 degrees. Thus we have tan 45 degrees is equal to perpendicular that is A B upon base that is P A. Now A B is equal to h and P A is equal to x and we know the tan 45 degrees is 1 so we get 1 is equal to h upon x. So this implies x is equal to h. Now consider the right triangle C P A so in right triangle C P A here again angle C P A is given to be 60 degrees and tan theta is perpendicular upon base. So we have tan 60 degrees is equal to perpendicular C A upon base P A and here C A is equal to C B plus V A which will be equal to 1.46 plus h upon P A that is x and tan 60 degrees is equal to root 3 so we have root 3 is equal to 1.46 plus h upon x. Now we already got the relation that x is equal to h so here we will replace x by h so this implies root 3 is equal to 1.46 plus h upon h by cross multiplication we get root 3 h is equal to 1.46 plus h this implies root 3 h minus h will be equal to 1.46 that is taking h as common we will get h into root 3 minus 1 is equal to 1.46 this implies h is equal to 1.46 upon root 3 minus 1 now root 3 is given to be 1.73 so it will be equal to 1.46 upon 1.73 minus 1 that is 1.46 upon 0.73 which is equal to 2 thus the height of the pedestal that is h is equal to 2 meters therefore height of pedestal is equal to 2 meters and thus this is the required answer for this question with this we finish this session hope you must have understood the question goodbye take care and keep smiling