 Hello and welcome to the session. In this session we discussed the following question which says, the angles of elevation of the top of a building from two points on the ground at distances c meters and d meters from the base of the building and in the same straight line are complementary, find the height of the building. So according to the question we have a building whose angle of elevation from two points which are at distances of c meters and d meters from the base of the building are in the same straight line and are complementary, we have to find the height of the building. Let's see how we can do this. First of all we assume let this p cube be the building and we also take let p cube be equal to h meters. We have to find out this h and let r and s be the two positions of the observer and we have that the two points are at distances of c meters and d meters from the base of the building. So we take let q s be equal to c meters and r cube be equal to d meters. We also take let angle p s cube be equal to theta. So this theta is the angle of elevation from the point s of the top of the building. So this angle p r cube would be equal to 90 degrees minus theta since this r is also the position of the observer and we are given that the angle of elevation are complementary. So if one angle of elevation is theta the other would be 90 degrees minus theta. Now consider the triangle p s cube in this triangle p cube upon q s is equal to tan theta that is perpendicular upon the base. Now p cube is h so h upon q s which is c h upon c is equal to tan theta this gives us h equal to c tan theta let this be equation one. Next we consider the triangle r p cube in this triangle tan 90 degrees minus theta is equal to perpendicular upon the base that is p cube upon r cube. So tan 90 degrees minus theta is equal to p cube which is h upon r cube which is d so this means cot theta is equal to h upon d since we know that tan 90 degrees minus theta is equal to cot theta and so where we get h is equal to d cot theta like this be equation two. Now multiplying equations one and two we get x square is equal to c tan theta into d cot theta that is x square is equal to c d which means that h is equal to square root c d and we had assumed h to be the height of the building that is p cube is the building and p cube is equal to h meters so h is the height of the building thus we say the height of the building is equal to square root c d meters so this is our final answer with this we complete the session hope you have understood the solution of this question.