 Hello and welcome to the session the given patient says from a window x meters high above the ground in a street the angle of elevation and depletion of the top and foot of the other house on the opposite side of the street are alpha and beta respectively. Show that the height of the opposite house is x into 1 plus tan alpha into cot beta meters. Let's start with the solution and in this figure let CD be a window and AB be the house which is on the opposite side of the window. Now the angle of elevation is alpha from where he is observing the top of the house is point T and from the same point is above observing the bottom of the house which is the point B and the angle of depletion is given to us as beta so this implies this angle is also beta. We have to show that AB or h is equal to x times of 1 plus tan alpha into cot beta meters. So let AB be the house and we are supposed that AB is equal to h meters also DC is given to us as x meters which is the window above the ground. Now let us suppose that BC is equal to y meters and this implies BC is equal to ED is equal to y meters. Now let us see in triangle EBD. In this triangle we have EB divided by ED is equal to tan beta and the distance EB is equal to x meters since EB is equal to DC which is x meters. So from here we have x divided by y is equal to tan beta which further implies that y is equal to x divided by tan beta. Let us denote this by equation number 1. Now let us see in triangle AED here we have AE divided by ED is equal to tan alpha which further implies that h minus x divided by y is equal to tan alpha or it can further be written as h is equal to x plus y tan alpha. Now in substituting the value of y from equation number 1 we have h is equal to x plus x divided by tan beta into tan alpha and this is from equation number 1. Now we have h is equal to taking x common 1 plus cot beta into tan alpha thus the height of the opposite house is equal to x into 1 plus tan alpha into cot beta. So this completes the session hope you have understood it bye and take care.